Shitty Ask Lemmy

It really depends on the time of year. If you come in the fall, the state fair is a must-see -- it's usually at the top of lists of the biggest, most popular state fairs in the US. Late summer, I'd spend time on the lakes, especially Lake Minnetonka. Go to Wayzata and Excelsior, or take the old restored Lake ferry between them. Minneapolis has some of the best bicycling infrastructure in the US; especially focus on the converted LRT trails. There's a ton of stuff to see in Minneapolis, but there's a bunch of cool stuff in St Paul, too. Not knowing your demographic of time of year you're visiting, here's my generic list for touring guests:

• The Flour Mill. Downtown Minneapolis, historic, good source for brief history of Minneapolis, and central for seeing other sights. You can walk the shores of the Mississippi and hit downtown while you're there.
• St. Paul Cathedral. Big. Dome. A metric ton of stained glass. Bigger than many cathedrals in Europe. Nearly always open, and free.
• St. Paul city hall. Outstanding art deco architecture. Good for a half hour. Usually closed except during business hours. The law library at the top is a hidden gem with amazing views, especially if you like books.
• Wayzata. Good introduction to Lake Minnetonka, the biggest body of water near Minneapolis. The train station is a little museum with history of the city; it has limited open times, but the rest of the city is mostly restaurants and shops and will be open over the weekend. It's free parking and walk the entire thing - it's not huge.
• MN Landscape Arboretum. It's like a tiny Longwood Gardens, if that means anything to you. Good for a couple hours, or more. The Christmas lights are probably down already, and depending on weather there may be limited access unless you have cross country skiis. It's free, but parking costs; however, there's a free park-an-ride shuttle, too.
• Excelsior. A larger, more livable Wayzata on the other side of the Minnetonka. Some shopping, some good restaurants, nice lake houses.
• Walker Museum, not free, modern art
• MIA (Minneapolis Institute of Art, free), a large traditional (historic) art museum.
• Carver County Park. Massive park with some historical sights. Mainly good for walking and biking. Miles and miles of trails.
• Minnehaha State Park. Best in the summer, still worth seeing and far less busy in the winter. In the city, and runs along the Mississippi.
• Eat street, the colloquial name for a section of Nicolette Ave. It's a mile of bars and restaurants covering everything from German, to Greek, to Thai, to American... just about every kind of cuisine you can imagine.
• Aside from eat street, there are some excellent, expensive, restaurants in Minneapolis
• The Minneapolis Public Library is an amazing space. Highly worth a visit.