If you're fit and you love fresh air, you should consider touring Munich, Germany, on a bike. Like many European cities, Munich is very bike friendly and has wide, clearly marked bike lanes crisscrossing most of its major streets and thoroughfares. Biking in Munich is much safer than biking in most American cities, especially since many bike lanes are on the sidewalk rather than the street, and other bicyclists and motorists are very conscious of local traffic laws. Biking allows you to cover more ground that walking, but on a bike you'll still be able to stop and check stuff out without worrying about parking. Plus, biking is very popular in Germany, and you'll fit right in when locking up your bike outside of museums, bars, and anything else you want to visit.
If you have experience biking in American cities, especially New York, you may be accustomed to doing whatever you think you need to in order to arrive at your destination alive and in a timely manner, including running lights, biking on the sidewalk, going the wrong way up one way streets, and weaving in and out of traffic. That kind of behavior won't fly in Germany, where the people are seemingly even more concerned about upholding the law than the police are. You'd better stay in the bike lane on the right side of the street if you don't want the locals yelling and shaking their fists at you. Obey all traffic laws and don't ride abreast with other cyclists.
You also may be surprised to learn that Germany has very strict laws about your bike equipment. You don't have to wear a helmet if you don't want to, but your bike needs two independent braking devices, non-blinking head and taillights, reflectors, fenders, and a bell. Fixed gears are illegal. Transgressions will result in heavy fines, and the German police are known to stake out busy bike lanes so that they can bust people for broken lights and rusty bells.
It's very easy to find a bike in Germany, since the Deutsche Bahn has a public biking initiative that rents out bikes from stations all over the city. This Call a Bike program is an automatic service that works via cell phone and costs nine euro per 24 hour period or eight cents per minute. These DB bikes will mark you as a tourist, though, since they're a bit conspicuous. If you want to blend in, you can spend about 15 euro and rent a cooler looking bike from nearly any small bike shop that you see.
Germany can get cold and snowy in the winter, and unlike in the States, people generally don't clean the sidewalks and salting is illegal. If you don't like the idea of biking on a six inch thick sheet of ice, plan your Munich biking adventure between May and mid November, when you probably won't have any adverse weather conditions to deal with. The city of Munich offers a free, downloadable, English map of all of the bicycle lanes and routes, so it should be very easy to plan your own tour.