What are the don't-miss spots in Burlington, VT?
The factory tour at Ben & Jerry's in Waterbury (Waterbury is about 25 minutes from Burlington, not a difficult drive or hard to find at all) is something I always enjoy. I bring visitors there and have been through the tour many times. Kids will enjoy it, for sure. Even if you choose not to do the tour, there's stuff around the plant itself you can do, and in the summer there's snacks and lemonade stalls outside. Kinda like a mini carnival sometimes. :) They also have a scoop shop on premises (of course) and a nice gift shop with lots of different styles of things including food/chocolate stuff.
If it were fall I'd recommend Cold Hollow Cider Mill (not far from Ben & Jerry's) because they'd be pressing cider, but I still recommend it though less heartily as a nice gift shop and fun spot with interesting olde tyme equipmente to see. Loads of Vermont products, and not all of them are at tourist prices. I go to Cold Hollow to buy my cider, for instance. It's cheaper than at the store. They also make to die for cider donuts... oh god I need to make a trip at lunch tomorrow now. It's your fault!
I do enjoy the Cabot Cheese and Lake Champlain Chocolates outlet shops, too (also in Waterbury, between Cold Hollow and Ben and Jerry's). The whole bally lot of four shops is a very nice little trip and all are close together. They all feature Vermont products (as do loads of other sorts of shops, like the glass blowing studio near these two outlets and on the same road, but there's nothing to EAT there ;). There's a couple of farm stands and food coops on that same road, as well.
Honestly, for ice cream, I head down to Montpelier's Dairy Creme (http://www.dairycreme.com/). They make my favourite creemees. I'll probably be getting one of those on Friday while I'm out and about prepping for my trip to the UK this coming week.
In Burlington, there's the Echo Center (http://www.echovermont.org/), and there's lots of nice food carts in the area, and up the hill a bit there's a sorta cafe convenience store with a lunch counter. The center has a cafe, as well, but I wouldn't trust it to not be overpriced. It's also located right on the waterfront, and there's often events going on in the park that your child might enjoy. Generally at events, there's at least one decent food vendor, as well. :)
And of course there's Spirit of Ethan Allen dinner tours of the lake. But I think a young child might not enjoy that as much, though it's hard to say. Also might not fit with the 'inexpensive' idea.
320 State St, Montpelier, VT 05602