Congrats on the nuptials.
My input: You may have some snow. Definitely rent a cabin/room if you can. Been to Yellowstone many times, a few in early June. Snow every time. I'd suggest renting a cabin/room if you can, for that time of year.
In terms of wildlife viewing....yeah you'll see plenty of animals once you enter the park. Bison love to block the roads. I've seen grizzly quite a few times, closer than I'd like, bring bear spray. Lamar valley is good for wolf and grizzly viewing. Last time I was there watched a wolf pack fight a griz for an elk carcass. There is usually wildlife advocate groups set up with spotting scopes in the Lamar. Most of them will let you look through the scope. Or bring your own gear.
I've staid at most lodges in Yellowstone as well as a few campgrounds. Both solo, and with my wife. PM me for details. I can give some good ideas in the Tetons as well if you're up for a round trip option. Jenny Lake Lodge in the Tetons is an awesome romantic splurge....not cheap but amazing.
