To be clear, there are no RV Parks in Yosemite. There are only NPS campgrounds. No services. And my guess is that all campsites were booked within seconds of becoming available.
The closest camping that is out of the Park but nearest to Yosemite Valley would be on Hwy 140 around El Portal. See this website: http://jrabold.net/yosemite/campn.shtml I have no comment about which one might be "best."
If that's where you end up staying, you might drive into Yosemite NP on Hwy 41 via the South Entrance and visit Glacier Point area attractions on your arrival day. Then drive down, stop briefly at Tunnel View (your parking is on the RIGHT), continue into the western end of the Valley. then leave. On your full Valley days, drive in and park in a good location each day. Plan to walk or ride a bike to get around.