I'm a single parent and kid's dad lives about 40 miles away. When kids were younger I was lucky that they could stay with their grandmother since she was retired with a few camps thrown in because you're right, these camps are fucking expensive. When my daughter was old enough, they could stay home alone with random camps thrown in. We still try to keep my son, 10, busy with camps but we stick to those put on by the City Parks department or the Y. Swim lessons through the city is something we do every year as well as Vacation Bible School, add in a handful of weeks with the city camps, a week with my parents, a week with family in Rockport and it only leaves a couple weeks where they're not signed up for anything which I think is good for them. I think every kid should get to spend some time doing absolutely nothing in the summer.
Start summer camp planning early. It's too late for this year to start early, but this is something you should put on your radar by February. Sign up for some camps start in March. I usually have to create an excel spreadsheet with the weeks of summer and plot everything out. It's color coded for each kid too. I didn't do it this year. They're 10 and 15 and I was over it.