Go to, the Fargo Theatre, walk along the river starting at the path in Lindenwood, the Uptown Gallery, the Plain's Art Museum, the Hjemkomst Center (in Moorhead) has a German Culture day in September 19.
We've got a lot of bars and restaurants. Try the Würst Bier Hall, the HoDo Lounge, Nichole's Fine Pastry, Rustica (In moorhead, just across the river), Passage to India has really good lunch buffet that is $12 or less and has great, fresh, homemade things, and India Palace has the best entrees for dinner. Bangkok Corner is another good place. As someone who's been in the service industry for years, these places are the best in town.
Definitely check out the Aquarium above Dempsey's. (Dempsey's is a bar on broadway. It's welcoming to GLBT crowds and everyone else, and if you take the stairs to the left at the entrance, there are usually shows in the bar called The Aquarium. There aren't any signs for it.) The Würst is another good bar--get a boot there. Sit on the patio at Sidestreet. Go to the rooftop at Rhombus Guys.
Depending on the time of year, there is a drive from North Fargo into Moorhead that is usually very pretty. Right now there are fields and fields of sunflowers in bloom.
There is a zoo in South Fargo, and a lot of little shops in the downtown area with local products. Also in the summer there are several farmers markets a few times a week.
The Plain's Art also houses the Katherine Kilbourne Burgum Center for Creativity. There are events at both places, but the Center for Creativity often has one day courses like "clay for couples" and for a small fee you can use their facilities and have access to an instructor. It's really fun.
If you like lively, informed, and informal discussion, check out the NDSU Science, Religion, and Lunch Seminar. It's held during the school year and has members of the local universities faculty, students, and many members of the public. Every Tuesday there is a presenter on some (usually controversial but always interesting) topic related in some way to science, religion, or otherwise relevant current event. Then there is a discussion. You don't have to participate, but you can. It's a more cultural experience than eating and drinking.
Take pictures in front of the Iver's and the Prescott apartment building, and in the alleyways downtown. And by the trains parked by Broadway and Main Avenue downtown. It's what all the locals do... From there take a walk on 8th street starting from downtown, or in the Hawthorne District and see our old houses.
Check out a local alternative newspaper, The High Plains Reader (HPR1.com) for events while you're in town.
The time of year you visit. Depending on your tolerance for cold, winter can be really beautiful here. People go sledding on the dike and are generally extremely friendly. Maybe avoid January and February, as these are the coldest and (from my experience) we are all pretty affected by the winter by then.
Check out the Scandinavian store in the West Acres Mall, Stabo, and try the Rising Bread Co. I live and work downtown so I'm partial to it. South Fargo can be a sea of commerce and chain stores.
I hope these ideas are helpful.