I love the Minneapolis Institute of Art, and I hear the Walker’s newly re-opened sculpture garden is fantastic. As you can see from this map, the Walker and Mia aren’t super near what I would truly consider downtown Minneapolis (represented by the Minneapolis Visitor Information center, which is in the heart of Nicollet Mall). Perhaps the Hyatt Regency would be a good place to be to stay since it’s literally in the middle of the three spokes on the map? I personally would recommend staying somewhere like the Radisson Blu Downtown or the AC Hotel by Marriott because you’ll have the whole downtown to walk around, you’ll be a light rail station or two away from more theaters, eateries, etc. across the river (there’s about four on West Bank by the University of Minnesota alone) and, if you want, St. Paul, and then you can just get an Uber on the days you really want to go to the Walker or the Mia.
(In general, the buses and light rail tracks weave through the city pretty thoroughly, so if you don’t want to worry about parking as much, try using the Google Maps app (or the like) to figure out how to get through the city in real time.))