Go to thedailypage.com, which is the website for "Isthmus", Madison's weekly newspaper. At the top, click on "The Guide". Literally EVERYTHING happening in and around town will be listed. And if you click "Eats", you'll find the restaurant guide where you can search by meal/location/food type, etc.

You're in luck! There will be jazz on the Memorial Union Terrace Friday night. The Tim Whalen Nonet is performing from 6 to 8 PM.

Get there early, though, if you want a table. It fills up fast once we are all out of work.

This is outdoors, right on the lake, and there is food and beer available for purchase on site. Madison's best location for music in the summer.

AND if you're flying in on Wednesday, there is Jazz at Five outdoors in the 100 block on State Street.

As far as breakfast restaurants with good omelets, I agree with checking the Daily Page. My favorites downtown are Marigold Kitchen, which can be a little loud inside, or Sunprint, which has a larger, more pleasant space.

Both of these require you to order at the counter, but they use a lot of our local produce, which is all in season right now, so your timing is good!

Sardine, which only serves brunch on Saturday and Sunday mornings, is good if you're staying that long.

I hope you enjoy your visit. Post again if you have more questions. Glad to help.