It's fun to stroll State Street between UW and the Capitol. Sit out on the Memorial Union Terrace and watch the Lake.

Agree with abram. Standard attractions here include the capitol building (well worth a visit), the Wisconsin Historical Museum, and the Madison Museum of Contemporary Art. All are close by each other.

I agree with the above. The ultimate Madison experience begins at the Memorial Union Terrace. It is a great people watching place. I love watching people learning various water sports. It can be quite entertaining. Take your sunglasses and a book, kick back and relax.
http://www.union.wisc.edu/venue-muterrace.htm

No trip to Madison is complete without a walk down State Street from the campus to the Capitol. Lots of interesting little shops. Go into the Capitol and look around. It is a very beautiful building.

And if you happen to be free on Wed. evening it is time for Concerts on the Square
http://www.wcoconcerts.org/performances/concerts-on-the-square/
or
Saturday from 6AM until 2:00 PM the Dane County Farmers’ Market on the Square is a tradition in Madison

I think that Monona Terrace is worth a walk through as well. It was originally designed by Frank Lloyd Wright but took years and years to finally be built on the shore of Lake Monona in downtown Madison. The roof top is lovely and sometimes they schedule dances and music up there during the summer.
http://www.mononaterrace.com/contacts

The Madison Museum of Contemporary Art (mentioned above) is in the same building as the Overture Center for performing arts and there are often small entertainment/ activities scheduled there as well as large ones. Lovely building.
http://www.mmoca.org/
http://www.overturecenter.com/

Not sure of your exact dates but here are a couple of possibilities:
Restaurant Week:
http://www.madisonmagazine.com/Madison-Magazine/Events/Restaurant-Week/Restaurant-Week-2011-Summer/
or
The North American Unicycle Convention and Championships (NAUCC) will be held July 23-30 in and around Madison
http://uninationals.com/

All is easily walkable. I wish you fair weather.

Thanks for the replies.

Will get a printout of the list of to-dos as highlighted above!

yes, i will be there at restaurant week too and shd be able to make it wed evening for the concert.

not sure if i can make it for farmer's market but it seems like a big thing, hope i wont miss it too!

hope my first trip to US will be great, ta!

mdwest, thanks for the link on Restaurant Week. We will be there part of that week for orientation-good timing!