Reichenau is an island on the Bodensee/Lake Constance where the monastic tradition dates to the 800s. The island has three remaining churches that date to the 11th/12th centuries, and some original paintings remain.  The island has built small museums by each church with some information— however, it was a lot less history/information/signage than nearby St. Gall  

I visited St. Gall and Reichenau in a single day by rental car from Zurich. Both sites are about an hour from Zurich and an hour from rich other. It’s possible to do the same route by train, but the Reichenau train station is a bit far from the island — it’d be about a 3-hour round trip walk from the station to the furthest church on the island, so I felt I’d be rushed to do both in a single day without renting a car. It’s a popular cycling destination, but I didn’t see places to rent bikes on the island. 

As others helpfully pointed out, St. George is only open May-September twice a day by guided tour to protect the paintings. The tour times are still 12:30 and 16:00 daily. I confirmed the times with the visitors center before my trip. Unfortunately, no one shows up for the 16:00 tour the day I visited. No sign on the door/note it was cancelled. A group of 12 of us waited, myself for 30 minutes, before giving up. That was disappointing to say the least. Hopefully others will have better luck. (Note that the church, and not the tourist center/museum, runs the tours.)