Why not create a list of things for them to do!!!! You could simply print off the list below and check them off as you go through the summer, or perhaps schedule them all in to your calendar ahead of time, or if you are really spontaneous you could print the list and cut each thing out, fold it, and stick in a jar to draw out 1-2 items to do each day of the summer.
What we are doing is creating a binder with 100 individual page protectors with a heading on each one for each item. I will include this list on the cover of the binder so we can pull it out and cross it off as we enjoy our summer. On each page I will have a heading for each of the 100 items. I used lined paper (glued the colorful heading on - making this is also another item you could add to the list) to encourage my daughter to work on her writing skills. By using page protectors, she can add items that would be too hard to glue (like a badge from a Lowe's Build and Grow, which I should have totally added to the list.)
I wanted to make this a portable and easy to use binder, so I found a pencil case that attaches to the rings and filled it with colored pencils, a pencil, scissors, an eraser, and a pencil sharpener. It will stay in there and will be ready to write or draw pictures whenever we finish something.
I also included a pink piece of paper in the more time consuming field trip type items so that she has more to write/draw on. And maybe at the end of the summer when I have printed pictures from all our adventures, we will try our hand at scrap booking. I have never been interested in scrap booking, but this might be fun.
The idea for this list originally came from Honest to Nod. Many of the things on my list are from this list, but because some things were not in our area or I wasn't sure if we would have access to some things I needed to change some things, which meant I had to type up my own document.