Madison is one of the most bikeable cities in the United States, with over 200 km of designated bike paths and lanes. The Capital City State Trail runs east from downtown and connects to a wider system of off-road paths. BCycle, Madison's bike-share system, has dozens of stations across the isthmus and the university area; short trips are inexpensive and the flat terrain makes cycling practical even for infrequent cyclists.
The isthmus — the narrow strip where almost everything a visitor wants to see is located — is thoroughly walkable. State Street, the Capitol, the UW campus, and the lakeshores are all within comfortable walking distance of one another.
Metro Transit runs bus services across the city. The routes are frequent on the main corridors (University Avenue, East Washington Avenue, South Park Street) and useful for getting to areas away from the isthmus. The university area is well served.
Taxis and ride-shares (Uber and Lyft) work well and are reasonably priced for a US city. Parking downtown can be frustrating and expensive on weekdays; most visitors are better off parking once and walking or cycling from there.