The gorgeous, colorful frescoes fill the Branacci side chapel from floor to ceiling and are both beautiful in and of themselves and an important breakthrough in Renaissance art. If you'd be interested in some background on the art and history of the place, bring along a Blue Guide or read up on Renaissance art a little beforehand -- it's worth it to really appreciate these images so you know what kinds of details and interesting symbols to look for.
You can walk into the church itself for free (which is a nice cool break on a warm day), but you'll have to pay a small fee and go around to the side entrance to get near the Branacci chapel. They have a movie that shows every hour or so that is definitely miss-able (although its cheesy computer graphics are pretty hilarious).
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