Pack a picnic and grab some wine! Concerts on the square is a great way to spend a warm summer night in Madison. Concerts are Wednesday nights in June/July---check the website for dates.
You can start putting blankets down at 3pm to save a spot. Most people put a blanket down and come back around 5 or 6pm. Traffic is terrible. If you can avoid it, I wouldn't recommend driving.
There are lots of food tents serving delicious food if picnics aren't your style.
If you run out of wine, head over to Square Wine Co. to grab another bottle!