How about the mall? Our mall doesn't have a real play area, but it has a bunch of "insert a quarter" mini rides. My kids don't know that they actually do anything. They just like to climb on them. Once, a nice man started digging in his pocket and was going to pop a quarter in. I told him he'd better not! He almost ruined it for us all!
They also like to look at certain stores, and walk around and be where so many people are.
But before we moved here, the malls all had play areas and they were our salvation.
Also, we go to play places without buying much food. When I had just one kid who could eat solids, we'd go to McD's and play for over an hour, then share an ice cream and play some more. Not bad for $1. Although that doesn't really help since you say it's a dietary thing. But we only went maybe 2 times a month, just to change things up.
Or just bundle them up and haul 'em to the park, anyway. In the Fall, we think 40 degrees is so chilly, but after a cold winter, it starts to feel not so bad. We just had a picnic when it hit 50 because it felt so nice to be outside!
Okay, so I checked your weather, and 33 is pretty cold for a high. But it looks like you're getting snow. Go build a snowman or find a sledding hill. It's a lot of work, but it wears them out and they'll either take a long nap or go to bed early, so you can make up for the time you spent bundling them up!