If you can get a room at Red's Meadow you'll be ahead on Day One trail time.
If not, Mammoth works and is cheaper and has much better food.
Take the bus to Red's Meadow and go north on the JMT. (It's easy to get lost in the maze of trails around Red's and the Devil's Post Pile. Ask for directions at the store.)
Aim for Garnet Lake and Thousand Island Lake.
A National Geographic Trails Illustrated #809 will get you oriented.
Google Earth will provide perspective.
They are Stunning, popular and a little busy. But if you head a half mile west of either one you will be by yourself. Cross country is easy. There is a lot to see. And if you like it, scout a bit, look at the maps, and you'll find a decade of travels in amazing country.
Or for a little more solitude look at the Minaret Creek/Shadow Creek/JMT loop.
You'll need a backcountry permit, but that can be covered later if you decide to go.