Myanmar is in the throes of big change, both politically and economically, so travelers are flocking to see it before it modernizes and becomes like the rest of Southeast Asia. People are soft-spoken but friendly and genuinely happy to interact with tourists. Prices, especially for hotels, are starting to rise. As you’re probably aware, winter is peak season so places will be more crowded and hotel rooms in demand.
In general, people visit Yangon, the temples of Bagan, Mandalay and the Irrawaddy River, the hill country around Kalaw for hiking and visiting hill tribes, and Inle Lake with its placid waters, floating gardens, simple rural life, and pagoda ruins. Not to say there aren’t other destinations worth seeing but you’ll have to decide what interests you and works with your schedule.
In Yangon we stayed in central Kyauktada Township, within walking distance of Sule Pagoda, the markets and colonial district. In other places, lodging was at simple, family-owned guesthouses which included breakfast. During our two-week trip we flew between the above-mentioned places on clean, modern aircraft with snack service and young enthusiastic staff (U.S. carriers take note). The flights at most took half-hour to 45 mins. We also had a 5-hour mini-bus ride between Kalaw and Inle Lake, stopping at Pindaya Caves.
Unless you have unlimited time and can bear the horribly pot-holed roads and antiquated trains and/or buses—try taking the “Circle Train” around the Yangon environs for a taste—your best bet is flying. Road travel is slow-going and takes hours between even the nearest destinations. As for river travel, while I know there are boats specifically for tourists but whether you have to be part of a tour group, I can’t comment.
If you want a set itinerary prior to arrival (probably not a bad idea considering peak season), find a Yangon-based travel agent to book hotels and transportation. Alternatively, if you want to book your own hotels, go to asiatravel.com or booking.com. Once at your destinations, taxis, tuk-tuks or bikes are easy to hire for local travel.
ATMs are supposedly now available at the airport but there weren’t any last year. It was strictly a cash economy with only the largest hotels (presumably the government-owned ones) accepting credit cards. Bring cash and exchange as you go along; easy enough at hotels or with money changers (do count your bills before leaving).
Rough Guide’s guidebook for Myanmar (Burma) should help with other logistics.
Another good resource is Lonely Planet’s Thorntree travel board.