Aachen is a fairly easy city to get around in whether you are walking, take a taxi or choose to ride the bus.  It's old downtown area is very walkable, and in fact walking there is preferred to driving as the streets are small and narrow and there a lot of things to see that you will better appreciate up close.  If you get tired of walking though, there are plenty of taxis in the city.  Taxis can be hired by simply flagging one down off of the street, calling a taxi company to pick you up or by asking the doorman at your hotel to call one for you.  Taxis in Aachen are regulated by the government and have set fares.  Also, taxi drivers in the city do not generally expect to receive tips.

The city bus system in Aachen is very reliable and has extensive routes covering most of the city.  Bus stops are frequent along street corners and public areas.  Be advised however, the city buses stop running by midnight, or 11 PM in some cases.  See the ASEAG website for bus routes, fare information and hours of operation (in German).