We do animal exercises, DS loves that (there is also an animal exercises video on youtube we like, even though I don't normally allow TV, this seems to help when I'm not feeling creative -- it's called Sing, Stretch, & Shape Up I think)... also jumping on the bed, I sing 5 Little Monkeys and he will just jump, jump, jump!! We do A LOT of hanging upside down etc. -- if I'm worried about dropping him, I just do it over the bed/couch/across my legs/whatever. He loves 'rocket ships' too, which is a game I made up -- I lay on my back with my knees bent, and he leans into my knees (stomach in) and I count back from 10 & on "blast off" lift my legs (and him) way up into the air. I make up a lot of very physical games, I guess because that's how I best relate to DS.
Anyway, we also have a tunnel, soft balls, etc. and encourage their use in the house... as far as places to go, see if there are any greenhouses or ecotariums or whatever near you, those are fun places to run around a bit & avoid the horrible weather. I also have a group of friends I regularly get together with, and we each bring a couple toys to an empty room (program room at the library, church basement, whatever you can use) and let the kids go nuts. Also, a lot of malls have indoor play spaces (unfortunately none of the ones closest to me though!)
I am curious why you feel your DS isn't old enough for the playground? My DS has been enjoying it since he was ~8 months old.
Obviously we didn't go when it was super crowded and I stayed right behind him so he wouldn't fall or get trampled! But you might give it a try if there are indoor playground near you, and definitely the outdoor ones when the weather improves!!
Oh and as far as paid classes, I can't afford to pay for things like that but I have been able to attend a few free Music Together classes and I think that would be great for getting out energy too, they are very much about letting the kids express themselves however the music moves them.