If you are into World Flavor restaurants check out the ideas on this page http://www.visitmadison.com/visitors/dine/world-flavor/. L'Etoile, Weary Traveler, and the Essen Haus are all great. L'Etoile is a really nice upscale restaurant - http://www.letoile-restaurant.com/. I really like the Eno Vino Wine Bar & Bistro atmosphere too - http://www.eno-vino.com/modules/web/index.php/id/1

As for something to do on a tuesday:
The Ivory Room Piano Bar has live music tuesday - saturday and can be really fun if you like the piano bar scene.
The Majestic (http://www.majesticmadison.com/) and the High Noon Saloon (http://www.high-noon.com/calendar/) have live music most days. Check their event calendars for something that might interest you.

Check out more ideas for your stay in Madison at visitmadison.com!