You need to be a little more specific in what activities you enjoy and what you are looking for.
If you are interested in Palentology, northe east corner of the state. Malta, Glendive, Fort Peck, and Makosika.
If you like history, Custer Battlefield at Crow Agency, South Central near Billings, Bear Paw Battlefield Northern tier at Chinook, The old mining camps of Virginia City and Bannock in the Southwest.
Geology, The Lewis and Clark Caverns in the West/Central part of the State near Bozeman and the Berkly Pit and School of Mining in Butte.
Wildlife is just about everywhere, but some places have different species. The eastern plains are full of Pronghorn Antelope, Mule Deer, White Tail Deer along the River Bottoms, Hundreds of Bird and small mammal species.
Move to the North West, Glacier Park offers a good chance of seeing Bighorn Sheep, Mountain Goats, Grizzly and Black Bear.
Driving along the continental Divide and you will perhaps see Shiras or "Wyoming" Moose.
Yellowstone still has some buffalo, and lots of wolves. The thermal features are spectacular.
If you like horseback riding there are multiple business' across the state, and guided hiking tours. You can float the rivers in rafts, or shoot the rapids in kayaks.
Camping is great anywhere in the state, very different climates and vistas. I will say you will never see more stars than a moonless night on the high prairie.
Most of the rivers offer outstanding fishing for multiple species, both warm and cold water.
If you enjoy firearms there are a few manufacturers in the state including the Shilo Sharps facility in Big Timber,(South Central).
If you give a little more information about what you enjoy or would like to do, I can help with some points of interest, some not on the usual tourist spot maps.
This state is well worth exploring, But you won't do it in a week or 2, I have been exploring for a lifetime, and I am just getting started.
