The big tourist attraction there is the Last Supper. To protect its fragile fresco status--and the restoration, which took from 1978 to 1999--the church of Santa Maria delle Grazie only allows a small number of people in at a time, and you have to go through an intense series of climate-controlling entryways. At certain times of year, you have to arrange weeks in advance to see it.
We were there in the spring, which is high tourist season, so someone suggested that we book one of the bus tours that end with a visit to the Last Supper. They prearrange with the church for set blocks of time.
Now I'm much too proud an independent traveler to EVER take a bus tour, but it was the only way, so we did it. The guide ended up being lovely, and we got our 15 minutes with the Last Supper.
There's another church, called San Maurizio al Monastero Maggiore, that has lesser known frescoes that have also been restored.