Since you're willing to camp in the park and have a generator, I highly recommend Moraine Park. Centrally located to a lot the east side has to offer and gorgeous views, maybe not from your specific campsite but within an easy evening stroll. Hiking in the nearby Bear Lake area is some of the best hiking in the parks for families. Not too strenuous but you get right into the heart of some great glacially carved terrain.
You may already find it is very difficult to find an unreserved spot in July, esp. if you have a larger rig. When it comes to campsites around the popular NP's, these sites often sell out in few hours or few days after the reservation window opens. You might try limiting your stay to a Sunday through Thursday night to increase you chance of snagging a spot. RMNP is so close to the Denver area and environs, the locals snap up all the spots for the summer weekends pretty quickly.
The west side of the park used to be something I also recommended for those looking for the less crowded experience. The town of Grand Lake is something like Estes Park was 40 or 50 years ago. But alas, the beetle kill around Grand Lake, Granby Reservoir, etc. has really impacted the views and overall feel of this area. Definitely worth a drive over Trail Ridge Road for a day trip, though.