Park further away and walk the few blocks. Should be a nice day and the rates are a little cheaper. There are garages everywhere. Most bars/restaurants are on 7th I believe (not great on actual street names there). It's the road in front of Xcel and parallel to 35E. That's where you'll find places like Tom Reid's sports bar. There's a bigger place on the corner nearer the Xcel. Serves some big food portions, but the name escapes me. Many places will be packed so get there early.
The Savoy Inn is a must, but it's on the other side of downtown St. Paul where highway 52 ends. Great pizza. All the meats are homemade. Expect to spend a lot of time waiting for a table.