Rafting is available on the Kings river, outside the park. July is late in the season, they might be done for the year. There used to be rafting on the Kaweah as well, been a long time since I looked into it. The only other rafting in So Cal is the Kern River. Lower Kern might have some rafting that time of year.
Staying in SEKI, there are lots of campgrounds in the area but it is pretty late yo schedule one. Look at Princess, for some reason it tends to fill up last. Check site lengths on recreation.gov and look at campsitephotos.com. There some nice spaces at Big Meadow too.
There are private campgrounds outside the park, I am not a fan because they are st lower elevations and hot in the summer.
2017 RAM 1500 4x4 5.7 HEMI
2015 PCW ECON 18RBS