Yellowstone, depending on what areas of the park are open/closed, can be an awful tourist trap. Stay away from the main roads if you can.
Jenny Lake campground in the Tetons is awesome, but I think it's first-come first-served. You can check. I spent a couple weeks out there last summer, so my thoughts are if you're arriving mid week, you might find a camp spot. If you can get a reservation, do it, and do it well in advance. There are several camp sites in the area, you can't go wrong. We spent most our time camping backcountry at higher elevations, and permits are super easy to get. The ranger station has bear cans if you go that route, although all you really have to worry about up high are the marmot. They chew backpack straps if you're inattentive. There are even bear lockers at some backcountry sites. All the camp sites around Jenny/surrounding areas have bear lockers. Have fun - I'll be back out that way early June, too!
Edit: re specific camp sites: I think the reservations.gov or whatever the website is should have pics of most of the camp sites as you're making your reservation. I usually refer to the campground layout map and individual site pics to get an idea of which sites are best, ie close to bathrooms = high traffic noisy area, or convenience, depending on your preferences.
Edit 2: 3 days at Yellowstone if you enjoy walking around gabs of typical Americans, yokels in jean shorts, and girls who shouldn't be wearing mini skirts. That's my opinion, though. I prefer trees to people.