T.H.
My daughter is two and half also and I just started teaching her card games. We've only played Crazy 8s and Go fish, but she has a really fun time! You have to have more patience than normal b/c they really don't get it at first, but even after just a few times, she's really catchting on! I'm going to start introducing her to board games soon too I think. We also like puzzles and she LOVES to help me bake.
My boy is 8 months so I can relate totally. Although I'm not necessarily advocating this, I did sometimes throw his nap schedule to the wind (which I NEVER would have done with my daughter) so that I could take her to a play date, activity, whatever, b/c I just couldn't take it anymore! I'd say a few times a week we stay home for his napping and a couple days we go out and he either naps on the go or sleeps when we come home. It was a very hard adjustment for me to go back to the multiple naps and much more needy schedule. Once I tried to compromise both their schedules I felt a lot happier, and that's half the battle! ;)