Not sure what your town and local communities have to offer like, Museums, Art gallerias, Universities, Gardens. Parks, Historic places, concerts. Get out a calendar and schedule small outings. Take a cooler so you can eat at a different park each time.
Make up a schedule of events.
See if there is a Red Cross Babysitting class. She could then babysit, young children or elementary aged children. Take a first adide class together.
Also find some places to volunteer.. at least once a week.
Think of a home project. Paint her room, paint a pieces of furniture and sell it on craigslist. Work on making the back yard a fun area. A place for meals, a place to entertain.
We used to plot out the summer movies so we would know what movie to see that week.
Have her plan at least one meal a week. Give her a budget.. She can go grocery shopping, then Have her make the meal. If she enjoys being creative, have her set up the table.. Our daughter loved using our good china.. etc.. for meals.
I have been getting back into cross stitching. I do not do the traditional..
I do The humorous, or subversive cross stitching. I make them and save them for when I need a funny gift. I place the stitching in a frame.
Have her design Christmas cards for the family, or little Christmas gift tags.
Our daughter used to design tshirts. She would either draw them or do them on the computer and then purchase the iron on transfers.. Tshirts can now be ordered online for pretty cheap.. so she could email her designs. Make sure her signature is on them, so she can prove she designed them.
I had a friend that liked to have her kids do science projects during the summers. They would then take notes, photos etc.. so that while the Science fair was going on during the actual school year, they could then go through their summer projects and compare results etc.. They had more information and knew what science projects they wanted to do.
Have her organize the family photos.
I have always wanted to learn to knit. Our daughter learned while in High School.. She and a group used to knit scarves.. to donate.. There are so many great patterns..
I love Pinterest for inspiration.