None of the MIA airport hotels are cheapish, but there are a dozen near the airport. The Marriott is pretty good if you want something plush, also has frequent and fast shuttle service (some of the cheapest hotels are horrible for shuttles, to the point that you may need to use a taxi to make your flight -- making them not so cheap after all). Also the Marriott has 2 cheaper chains next to it (actually on the same property (clever idea, building 3 hotels instead of one, differentiating the market). They all share the same shuttle bus.

The in-terminal hotel is poor and very expensive (but no bus needed, you walk to check-in).