If you get hot doing the walking around thing, there is a public pool in Truxtun Park. If DC requires a swim diaper, they are pretty strict about kids wearing "ecology suits" - which they sell for $6 - over the swim diaper to keep the pool cleaner.
Anyway it is in a nice spot near the head of Spa Creek (there is a boat ramp) and there is a playground on the other side of the parking lot.
http://www.annapolis.gov/Government/Departments/Recreation/Parks/SwimmingPool.aspx

When I go to Annapolis it's usually by boat so the priorities are fresh ice, cold beer and a good meal. The BoatYard is nice and casual and walking distance from East Port boat marinas...we usually hit the Middleton Tavern for oyster shooters, and they have a kid's menu, it's right at the center harbor area.

I would do one of the boat rides, maybe the pirate boat cruise or even the tour around the harbor. Lunch either at Boatyard Bar and Grill (great food and family friendliness just in Eastport not in downtown Annapolis) or Buddy's right in downtown (the family friendliness and location outweighs the food here). Get some ice cream, maybe window shop some. Then I would hit Annapolis Mall on the way out just to get some indoor exercise time. There's a train ride and a great indoor playspace outside Pottery Barn.

Even though it will be hot, last weekend was even hotter and downtown Annapolis was still busy with tourists, just not as many. We went downtown on Saturday for ice cream around 4 and the boat cruises were full, parking was tight and plenty were walking around as usual.

Thinking of doing a daytrip to Annapolis with my 2 year old on Saturday -- can anyone suggest things I might be able to do to with her there??

It's supposed to be kinda hot so I'm not sure if there are any indoor things we can do or whether this is a good idea at all. Would love some thoughts!!!!!