For options close to the wedding venue
There's a viking ship in here, what more do you want?
Catering for the reception, so a very strong recommendation here.
University of Wisconsin Graduation is the same weekend as the wedding, but if you don't mind the mess of traffic and parking, here are a couple options. Restaurants not listed, as we expect them to be fully booked all weekend. If you would like any downtown restaurant recommendations anyway, please contact us directly.
Beginning April 13 and going through November 9, there is a Farmer's Market on Capitol Square every Saturday morning
Designed by Frank Lloyd Wright, Monona Terrace is right next to the isthmus, and has tours and exhibits in addition to being an event venue.
Not FULLY downtown, but close enough that it may be very busy that weekend.
If you don't mind a bit of a drive, here are some options for fun day trips in the area.
Museum which catalogs the history of the many circuses in Wisconsin.
The Troll Capital of the World.
Brewery which creates some much-loved Wisconsin beers, including Spotted Cow, its most heralded local craft beer(which will be on tap at the wedding)! If you're driving and would like to stock up on options which are not shipped outside the state, stop by!
If you've read American Gods by Neil Gaiman, you will be familiar with one of House on the Rock's attractions, but it's a fascinating and very strange place beyond that and is well worth a trip.
The Dells can be a full vacation in and of itself. There are all sorts of things there, from waterparks, to shopping, to tours, to live entertainment.