What do you think of as 'cheap'?
I live in Michigan. No-one from the UK thinks of it as a holiday destination but it very much is. There's 4 of the 5 Great Lakes, loads of outdoor activities & the weather is almost guaranteed 80 + in August, although just starting to cool off now.
At this time of year you can rent a holiday cottage for just over $1,000 a week, right in one of the lakeside towns. There's mix of hippyish/boho seaside, cheesy tacky seaside & some incredibly expensive 'naice' towns with equestrian clubs and sailing clubs. There's also loads of camp sites if you really want to keep costs down and can bring tents with you.
Depending where you go, there's sailing, beaches, snorkelling, surfing (you need wetsuits though, the big lakes are COLD even in summer), jet-ski-ing, kayaking, hiking, biking, rough camping on uninhabited islands, posh hotels, etc. We were thinking of doing the east coast, Cape Cod type thing, then realized that we had all the things we wanted to do in Michigan, so just drove.
You would need a car, though. If you fly into Detroit (DTW) you could also do some stuff there, like the Motown museum, art museum, Henry Ford & factory. But that gets more expensive. Chicago is another place to fly into, although you'd have to drive around the south tip of Lake Michigan (the armpit of Indiana) to get to the east side of Lake MI. There are pretty little coastal towns all around the lake, and if you head to the Upper Peninsula it can be very wild and remote. Chicago is also a great city to spend time in, loads to do, but as expensive as NYC.
I had no idea what this place was like until we moved here, but now I think of myself as extremely lucky to live by the Lakes. I'm a teacher and my summers are 3 months of sunshine and messing around in water.