Subie,
You may want to look here: www.madisonbiking.com to hook up on some casual group rides. They are not the hammerfests you read about on this forum. Not data-driven, friendly and often some refreshments. Also, I am a member of Bombay club, www.bombaybicycle.org which has organized rides. I'd encourage to check both out. I'm on the west end of Madison and I can assure you that once you get out of town you will see a lot of smooth pavement. University Ave is bad, but honestly, I don't ride on it much because the Blackhawk Path and Lakeshore Paths allow me to avoid it for the most part. There is also a path right along "Campus Drive" that you could take. I'd encourage you to pick up the Dane County and City of Madison bike maps which will also steer you towards better roads.

If you are interested in racing, check out the Great Dane Velo Club. They are racing the next few Sundays in the Research Park which is off Mineral Pt Rd and Whitney Way.