There are so many different things to do in Gainesville that it's hard to say what you 'must' do. It depends on what you like. There are three very nice and very different nature parks, two good museums, many interesting shops and restaurants, a thriving local music scene, art galleries and fine local theater, and the beautiful UF campus to explore. And, of course, there's usually a Gator sporting event going on...
Fondest memory: ...like the best college football in America. Gainesville blooms with orange & blue people and energy six Saturdays every fall when the mighty Florida Gators take the gridiron. Florida Field is the largest arena of any kind in the entire state, and instantly becomes one of the 10 largest cities in Florida on game days. The Swamp (as it is affectionately known) has been repeatedly voted as the best atmosphere for college football in the nation. There is nothing like the noise, thrill, and sheer exictement of a Gator game, even if you don't know much about American football. Buy a ticket from some poor student, put on something orange or blue, and yell until you lose your voice. 90,000+ people can't be wrong; it's a blast!
Gainesville is the coolest town I've ever seen. A real collage town, all young people, many nice bars and places to go.
The first time I vistited Gainesville during a Football-Game Florida Gators vs. Miami Dolphins. Everybody went crazy, many people had their BBQ and TV's at the side of the road.
The second time was much calmer but still very nice.
Around Gainesville is much nature, hot springs and nice areas.
Favorite thing: Most people that visit Gainesville do so either to visit a student at the University of Florida, watch a Gator football game or visit the excellent Sands Hospital. Well Gennie Spring is worth a visit. You can float down the river in perfectly chilled water. Floats can be rented at the dive shop. Camping faciliteis are also in the grounds. Gennie is also well know for it's cave diving. If your are certified for cave or cavern diving they have several interesting caves at the spring. Scubea equipment can be rented at the well stocked dive shop.