I've edited this to move the most pertinent info addressing your concerns to the top.
The sandflies are not that bad, just bring repellent. The only place where I've had a problem with sandflies was on a West Coast beach (somewhere between Haast and the glaciers) where a fresh water stream flowed out to the sea. But I was in Greymouth, which is also on the West Coast, a few months ago and spent a long time by its wetlands and never got bitten. i don't get it. I try to keep moving, cover up, wear repellent. Here's a good article about the dreaded sand fly:
It'll be all right, flying into Queenstown and starting your journey there. Ask for window seats! The view from the jet is breathtaking (if clear).
It's cheaper to rent a car and drive from Queenstown to Auckland, I think, because so many people do the opposite and the rental car companies need their cars returned to Auckland. You are helping them out, so they give you a break on the rental. Jucy rent-a-car calls these "relocations" and they offer astonishing breaks on these rentals. See:
As I said, there are no guarantees with the weather, so it could just as easily be stunningly perfect weather at the beginning of January. Besides, the mountains and lakes of the South Island's interior are so forgiving, they look magnificent whether it's rainy or sunny. On the other hand, coastal areas can be miserable in the rain.
But it never stays cloudy or rainy for long, you could experience four seasons in a day.
I don't think you should change your plans. Just be aware of how it will be so that you aren't surprised or disappointed The first time I visited Rotorua I was fascinated by the geothermal activity and the Maori culture in such abundance there, but I was dismayed by the tacky tourist shops and many motels. On my second visit, I knew what to expect so I mildly enjoyed the tacky tourist shops. I remember watching a Maori carver in one them, crafting delicate jade (pounamu) pendants with such artistry and skill, and, indeed, this is where some of the most skilled Maori artists are based. There are many in the Bay of Plenty and East Cape, as well.
Same with Queenstown. I go there now, knowing what to expect. On our last visit, we rode the gondola, which we had shunned because it seemed too touristy, but it was fabulous. The views are great. There are trails at the top, and your kids will enjoy the luge. Glamorous Queenstown is surrounded by wonderful scenery. It sits on Lake Wakitipu and looks upon the Remarkable Mountains. It's not laid-back, but lots of shops, restaurants and attractions mean convenience and choice.
So much to do in Queenstown:
If you need to escape the bustle, drive to Glenorchy, about 40 minutes from Queenstown, but a world away. Arthur's Point Road is also quiet. Take a drive up to Coronet Peak. Rent some bikes and explore the biking trails. Drive to the bucolic Gibbston Valley wine country. There are quiet little beaches around Lake Wakitipu. It's easy to escape from the busy center when you need a bit of peace and quiet. Plus, you can always retreat to the serenity of your accommodation and you don't have to stay in central Queenstown, you can find a vacation rental outside of town. There is an abundance of accommodation here, but it does get busy in summer, so book early if you find a good deal.
Chances are when you see Queenstown's shopping district, you'll think, "It's not so bad." Here's a You Tube that will give you an idea:
Wanaka isn't as busy, not by a half, but it still has restaurants, cafes, shops, supermarkets. It's a resort town, but also like a regular small nice town with spectacular scenery. It has a walkable, village atmosphere. It's popular with South Island families in summer, who go there to enjoy the lake's beaches, which are more reliably sunny, warm, and less windy than those of the coasts. You might want to spend three nights there instead, but it doesn't have the same attractions as Queenstown, so keep that in mind before you make changes. Wanaka is about an hour from Queenstown, but it would be a drag to have to travel this distance every time you would like to do something in Queenstown. There are two ways to get there: Crown Range Road or via Cromwell and the Kawarau River Gorge, both ways are challenging (more below). I am fairly certain that vacation rentals will be cheaper in Wanaka during summer.
There are some great drives here: the Crown Range Road from Wanaka to Queenstown is scary-exciting; and the drive from Wanaka through Mt. Aspiring Park to the glaciers is especially beautiful, particularly as it passes by Lake Wanaka and Lake Hawea.
Crown Range Road (the first few minutes should give you an idea of what it's like):
Do you plan on mostly going out for meals? (You mentioned walking to restaurants.) Because I'd assumed you'd want to self-cater. There are no restaurants in Porpoise/Curio Bay. There aren't that many on the Otago Peninsula, either, though there are a few on the harbor side. Curio Bay and the Otago Peninsula can feel like the end of the world, were it not for other tourists. There isn't much commerce.
Even if you plan on mostly going out for meals, it is useful to have a kitchen to make breakfasts or snacks. I often prefer my own preparations to those offered in restaurants or in B&Bs. For drive trips, it's useful to bring along a cooler for keeping food and drinks chilled.
Dining out can be costly in New Zealand. Here's a link to a range of average-cost eateries in Dunedin to give you an idea:
Nando's, a chain, specializes in rotisserie chicken basted with a spicy Mozambican Peri-peri sauce:
Shahi Tandoor is a cheap Indian restaurant in downtown Dunedin:
Speight's Ale House (pub food, part of the Dunedin brewery):
Zucchini Bros. is a local pizza parlor:
Fish Hook is a fish and chips shop:
Supermarkets often offer take-out items.
I went out to the peninsula today and noticed another farm stay:
It is near Allan's Beach, one of the nicest beaches on the Otago Peninsula, and the drive to it, on Highcliff Road and then beside Hooper's Inlet is wonderful (much is unpaved, but in good condition). Allen's Beach is about a 25-minute drive from Taiaroa Head.
There are sea lions on Allen's Beach, and sometimes you can see penguins. In summer, you can see many sea lions on the Otago Peninsula's Sandfly Bay (no sandflies here). This used to be a good place for watching penguins, too, but now it has the fastest declining YEP population on the Otago Coast due to human interference. Many penguins will not return to the beach if they see people on the beach, which is why you should sit down if you see a penguin swimming ashore. If they walk toward you, you should back away, as you might be blocking a path to their nest. The YEP is an endangered wild species struggling to survive, yet some people almost treat them as pets. They'll sometimes approach penguins or their nests, or harass them. At Sandfly Bay, the surfers, instead of taking the official track down to the beach, take a short cut through a steep hill used by penguins.
Today, at Allan's Beach, I stopped a tourist family from climbing up to penguin nests (the nests are located up steep hillsides that require a long climb to get to). I was shocked they even considered doing this! For its part, the govt. does little to educate people on how they should conduct themselves while viewing wildlife and it does not help that they have made deep cuts to the Dept. of Conservation. NZ is not like the US, where you often see rangers in parks. Anyhow, if you'd like to read more about the Yellow Eyed Penguin:
If you prefer to walk to restaurants, you might stay in Dunedin city instead, but in a quiet neighborhood instead of the busy center: St. Clair Beach or Roslyn. When in Wellington, stay in its center, so you can walk to Te Papa, the City Art Gallery, the cable car, restaurants, shops, the New World Market, Marine Parade. It's a good city for pedestrians, walkable. You'll like Coromandel, Nelson/Abel Tasman, Te Anau. Wanaka. You would have enjoyed the Bay of Islands, too. I wouldn't say that these places are funky, but they are more relaxed than Queenstown or Rotorua.
In Dunedin's St. Clair neighborhood, these holiday homes (within your price range, I think) are a few doors down from where I live (Earls Road), which is about a 10 minute walk to the beach, a swimming pool, restaurants, cafes, a small but adequate "Four Square" market, a fish and chips shop, bus stops. It is about a 10 minute drive to the city center (brewery, chocolate factory, museums, botanical garden, university, railways station and weekend farmer's markets), about a 20-minute drive to the start of the Otago Peninsula, another half hour or so to the end of the peninsula, where the albatross and blue penguin colonies are.
Earl's Road in Dunedin
Another St. Clair holiday house even closer to the shops and the beach:
This motel is right across from St. Clair beach and just steps to a few restaurants. It would be busy during the day, but quiet at night. Its rates might go up in summer.
Roslyn is another neighborhood with a village type atmosphere (shops, supermarkets, restaurants, mostly catering to locals).
I also came across these non-farm stay, reasonably priced holiday homes on the peninsula:
Otago Peninsula cottage:
Portabello (village atmosphere, not many restaurants):