I used to live in DC and went to B'More a lot but not with a toddler. I've been to Port Discovery, their children's museum, and it's hands on but I think it is more for older kids, like school age. The Aquarium is nice but you can't take strollers which stinks if they fall asleep on ya.
***October 08 Mama***
I was born and raised in Baltimore, so ask away.
I actually met another mama from my BB at Port Discovery (is the children's museum) 2 weeks ago. The kids had a ball. An older kid would appreciate it more, but 2 year olds love it too. Lots of hands on activities and there is a room just for kids 2 and under. Yeah, you can't have a stroller at the aquarium, but when we went last year (he was about 18 months) he was so into it that he barely wanted to be carried anyway. So I know definitely this year he would love it. And another good stop would be the zoo. You can make a whole day out of that.
If I can think of anything else, I'll let you know.