S.J.
Hi L.. My son will turn 2 in May and we spend a lot of time indoors during the day since I work from home.
One thing he loves to do is color. We have a little Thomas the Tank engine desk that's just his size and he will sit and color with his (washable) crayons for the longest time. He especially like it when I draw things for him to color, like Elmo, or a dog, or things he's familiar with. Crayola also make those wonderful Color Magic markers that only color on the special Color Magic paper. It's a bit expensive, but will save your furniture, walls, etc.
Mega-Bloks are also great at this age. They're big enough for little hands to hold, put together and pull apart without much help from Mom. He likes to build huge towers and gleefully knock them over. You can also get these pretty cheap at garage sales.
Wooden puzzles. I can't say enough about how cool these are. We probably have about 6-7 around the house and he loves taking all the pieces out and putting them back again. A good benefit is that he's learning his numbers and letters early while putting them in the puzzle one at a time.
Dancing is also fun with a 2 year old. Whether in a Kindermusic class or just you and him in the living room. The best part is that my son doesn't care how badly I dance (and I dance very badly) and it gets his excess energy out.
I could go on. :) Magnets on the refrigerator, riding the tricycle around the living room, giving his toys a "bath" in the kitchen sink, but those are more supervised activities and with 2 month old boys, it sounds like you have your hands full!