L.C.
For the energy part, there's a place around here called Monkey Bizzness which is basically a little gym place with slides and jumpy castles and stuff but it's for toddlers. It's "fenced" in so the kids can run around w/o the parents worrying too much of them getting "loose". haha. Also there are seats for parents so they can sit in the enclosure and keep an eye on their kiddos. Here, there are $5 Tuesdays where it's open in the evening from 5-8pm. (other times I think it's mostly open weekend days for free play). It's a really great place (and actually fun for parents too as we're allowed to play on the equipment as well!). I would suggest you check out places like that near you where your dd can go to run around when it's cold out.
As far as other ideas for busy activities, can you get her some kind of 3-yo science kit for a birthday or something? I feel like one of our freinds has that and it's pretty benign. That way she can feel like she's doing "science experiments" but you know she's doing them in a less-destructive way. Or...you could always cover all the walls and furniture in plastic and give her paints LOL! I feel you though, as we've got a 4yo and she definitely gets rambunctious when she wants more attention. good luck!