Minneapolis–Saint Paul International Airport: Take the METRO Blue Line, not a taxi, for downtown Minneapolis: it runs from both terminals to downtown for about $2, with roughly a 25-minute ride from Terminal 1. The inter-terminal train is free and runs 24 hours; confirm your terminal before setting off. For downtown Saint Paul, take Blue Line to downtown Minneapolis and change to the Green Line—slower, but far cheaper than a $20–$40+ rideshare.
Union Depot, Saint Paul: Amtrak’s Empire Builder arrives here from Chicago and the Pacific Northwest. For Minneapolis, use the METRO Green Line directly from Union Depot through Saint Paul and the University of Minnesota to downtown Minneapolis; allow about 45 minutes and a regular $2 transit fare. It is a handsome station and a genuinely useful arrival point, but it is in Saint Paul—not walkable to most Minneapolis hotels.
Hawthorne Transportation Center / downtown Minneapolis intercity-bus stops: Greyhound and Jefferson Lines use Hawthorne Transportation Center; Megabus uses the Ramp C area near Target Field. Target Field Station is about three blocks from Megabus and connects to the Blue and Green light-rail lines. Hawthorne is close to downtown but not a destination in itself: take a short rideshare after dark or use transit once you have your bearings.