Beacon Hill is pretty central, overlooks the park. However I would recommend staying in Copley Square area if you can - its closer to the main bus routes and the better shopping areas.
(Its 11 years since I was there BTW)
I can recommend the Marriott Long Wharf which is located right next door to the Aquarium and has a subway station right outside the hotel lobby. The Boston underground train network (the 'T') is easy to navigate and you can reach anywhere in Boston really quickly. The Marriott is within a few minutes walk of Quincy Market, Fanueil Hall and a great selection of restaurants. There is a Starbucks in the hotel lobby and an indoor swimming pool. Copley Square is also a lovely area but you may find the hotels there a little expensive. If you fancy a guest house then I believe that the Newbury Street Guest House is both centrally located and highly recommended. Newbury Street is the place to shop for designer clothes.
Jealous . We honeymooned in Boston. It's a lovely city. Take a whale-watching boat trip if you can - totally awesome! And we had lobster for the first time there, your 16mo would enjoy that: it's finger-food for adults. I think the restaurant was called Legal Seafood, or something equally weird, I'll ask dh when he gets home. Definitely recommended.