any bike rental places located in downtown Madison? Thanks!

It depends on how much bike you need. Here are the particulars, and the 100 number in the address indicates how many blocks from the State Capitol building each is located:
Budget Bicycle Center (no website, but worth the phone call) 930 Regent Street 608-251-1663
930 Regent St is Budget Bicycle Center’s Used Bike Sales & Bike Rental location; Budget has other locations on Regent St for clothing & accessories, new bikes, etc).
~100 rental bikes; will also negotiate long-term rental on hundreds (really)of used bikes
Madison’s Red Bike Program (run by Budget Bicycle Center) They loan out bikes for a $40 deposit for the bike and a $20 deposit for a lock. The user is responsible for the bike. When it is returned, the deposit is returned. If the key to the lock has been lost, there is a $5 charge.
(from: dir.civc.wisc.edu/view.asp… )
Williamson Bicycle Works & Fitness www.willybikes.com aka Willy Bikes
640 West Washington Ave 608-255-5292) ~30 rental bikes, including ~7 road bikes
Yellow Jersey www.yellowjersey.org
419 State Street 608-257-4737
6 rental bikes available, NO RESERVATIONS – first come, first served ONLY
Machinery Row Bicycles www.machineryrowbicycles.com
601 Williamson St 608-442-5974 ~40 rental bikes
We also now have commuter bikes to ride from one location to another in town, sponsored by Trek.... http://madison.bcycle.com
We got bikes from the kiosk on the lake. Great for an hour bike ride and very reasonable
We ended up renting there as well. Wonderful but crowded, so allow time for things to get sorted out.
And we can add BCycle for short-term rentals, sponsored by Trek:
Many pick-up locations downtown and on campus.