Kate Jones
Google
This is the main attraction in Passau. There is a shuttle bus to and from Romerplatz for 5£. (Well worth the time and effort to get here.) Passau is lovely, but there isn't a lot to do in the town.
There is a castle museum with portraits, church-y items, and castle doo-dads. Unfortunately, the castle areas themselves are not open. I was expecting to see the museum, then tour the castle, but that's not the case.
I guess it depends on your expectations, but we didn't find the museum to be expansive. There was a few chests, armor, weapons, Bibles, portraits, maps, etc. but not a lot of any one thing. Maybe not being able to enter the castle dampened our enthusiasm. We spent about 45 minutes in the museum, and another 45 minutes wandering outside.
There is a restaurant with a great view. Unfortunately, it stays packed, and suffers from oktoberfest syndrome. I've found most Germans to be rather dismissive of the idea of sharing a table. After trying about 20 tables and being told no, we just left.
Theoretically you can walk up to the castle, but unless you are an Olympic race walker, I wouldn't advise it. Gorgeous views of the 3 rivers, although one river is pretty dinky.
Set aside several hours; more if you want to go slowly through the museum.