My apologies that it took so long to reply. I'm just seeing this.
I'm the author of Frommer's EasyGuide to New York City and a mom of two. Here are some thoughts:
1) I hate to say this but I DON'T recommend staying near Times Square, especially with a toddler. Times Square is the part of the city that New Yorkers avoid because it's too crowded, with lousy and overpriced foods and constant crowds. It will be difficult to deal with if you have a stroller. Can you rebook? If you can, without losing money, I HIGHLY recommend staying on the Upper West Side instead. You'll be near Central Park that way, where you can go to decompress and play in a playground between sightseeing trips. It's also near a lot of the city's great museum. If you go to www.frommers.com/destinations/new-york-city/hotels you'll see all of the hotels I recommend up there.
2) I think your child would get very restless on one of the hop on, hop off busses, and I think they're overpriced with not great commentary. I'd recommend a two-hour cruise on the Circle Line instead (kids love boats) or just going out on your own.
3) Do try and go to the Statue of Liberty, but get tickets NOW if you want to climb up to the crown (which is a lot of fun). You'll also want to go to the 9/11 Memorial Museum (get tickets in advance), to the Metropolitan Museum, up to the top of one of our tall towers (you have three to go to (you can see all of the options at www.frommers.com/destinations/new-york-city/attractions). I've written that text and also divided the city by area, and given star ratings. Try to plan your days so that you're not criss-crossing the city too much. There's a lot to do uptown and downtown (slightly less in midtown, near Times Square---another reason to not stay there).
Again: apologies that my response is going up so late. Do write back if you have more questions. I'll post a reply.