If you need hookups, I'd recommend Mono Vista RV Park in Lee Vining. If hiking at high altitude is not an option, then definitely plan on driving Tioga Road at least as far as Olmstead Point, stopping frequently at the pullouts to enjoy the views.
You could also do day trips to June Lake, Lundy Canyon, and Virginia Lakes, all fairly near Lee Vining. If you and your vehicle are feeling adventurous, the ghost town of Bodie is north on 395.
Bring warm clothes -- the nights can be very chilly! The stars in the Eastern Sierra are amazing.