I'm not sure what our schedule will look like in September, but if I'm available it would be great to have a get together somewhere while you're in town.
As far as things to do, I'd strongly recommend renting a NiceRide (bike share bike) and riding along some of the bike paths and neighborhoods in the metro. https://www.niceridemn.org/
I'd check out neighborhoods you're interested in to get a feel for the vibe there. Uptown tends to have a more young professional hang-out vibe, downtown Saint Paul pretty much rolls up the sidewalk at 6pm, Northeast Minneapolis is cool artist/brewer/craftsman feel, etc.
There's a lot of cool stuff to see and do, but if you're looking at it for a place to live, I'd think about the things you like to do regularly and do those. If that's take walks by a lake, then check out some of the lakes. If its peruse the library, then head to the library in the neighborhood. I guess instead of looking at it from a tourist, think like a local. Check out the grocery store options (several co-ops, big grocery chain Cub foods, Aldi, specialty stores (butcher), etc.).