I booked my hotel before the Tribe clinched last night because I knew stuff would get booked up quickly shortly afterwards. I'm staying at the Renaissance, which is 5 mins away from the ballpark. I'm going down with a buddy, so we're splitting the cost which isn't bad. Hotel taxes are what kills you. Total for two nights was $550, so paying $225 each. If I find anything else better beforehand, could always cancel. Not much of a selection for AirBNB's as well (probably not that big in Cleveland as it is in cities like San Fran, New York etc).
Other options are staying outside the city around the airport, though you'd have to drive in for the games. If you just plan on going to the games, then that should be fine, though if you plan on going out for beers before & after the game, probably just best to stay downtown.