In September, I'd recommend Moraine Park. Elk gather in the large meadow south of the CG and you can hear them bugling from your campsite. RMNP has put together a map showing the RV lengths and whether there are mountain views from the camp site. Check out
this link. The campsites along the south end of loops B and C have the best views of the meadows with the elk and Longs Peak as a backdrop. Since B Loop is first come, first served, Loop C is your best bet. Reserve early as September is popular. Reservation system opens in late November for next season.
Another nice thing about Moraine Park is that you can use the shuttle system to get to the trailheads at Bear Lake and Glacier Gorge. Not having to drive and deal with the parking is nice.