Island Park is fly fishing mecca! The Henry's Fork River is in Harriman State Park! While, Mike and I don't fly fish so questions are better directed to Trout Hunter fly shop and guide service, they are located about 5 miles away from the park.
Drive to the top of one of the tallest peaks around! Sawtell is just 10,000 feet. It is about an hour drive one way from Harriman State Park. From the park, head north for 16 miles. Turn left at the Sawtell Resort/ Subway. Stay on Sawtell Road for 13 miles. Bring a jacket, it will be much cooler and winder at the top.
Yellowstone National Park is the backyard, well kinda depending on where you go in the park. There are tons of cool areas Old Faithful, Grand Canyon of Yellowstone, Mammoth Hot Springs, Norris Geyser Basin, etc, the park has a great app that has maps, hikes, guides, etc.. This is another good option for before or after the wedding. There is an app for phones called Geyser Times that predict times of geysers erupting.