There are plenty of hotels downtown Minneapolis. You'd want to open Googles Maps. On the search bar, type "hotels" and click on search. There are hotels within distance of Target Field. Stick to the ones on Hennepin Avenue and south of Hennepin, and close to 5th Street where the Metro Light Rail runs.
Depending on how much you are willing to pay for hotel rooms: Le Meridien Chamber Minneapolis $139; Hampton Inn & Suites Downtown Minneapolis $144; Hotel Minnepolis $100; Radisson Blu $194; Marquette Hotel $199; W Minneapolis - The Foshay $174; Grand Hotel $199; Westin Minneapolis $105 - these are just a few.
Think about taking the Metro Light Rail Green Line from downtown Minneapolis at Target Field, or at the Nicollet Mall Station on 5th Street and Nicollet Mall to the East Bank. Buy a roundtrip ticket from the kiosk to avoid the ticket line after the games.
I am parking in downtown Minneapolis and taking the light rail to the East Bank myself to avoid the craziness of the traffic after the game.