To get around Aachen is easy by foot, but should you travel with your old parents (the station is uphill on returning) or want to venture further out, buses are frequent and even go as far as Eupen in Belgium and to several Dutch villages as the border is only kilometres away which you realise by looking at the bike path signs everywhere. If you're travelling on a Land ticket by train from Cologne you can go on the city buses for free.
During our stay in London we usually flought (?) to other European destinations with Ryanair and Easyjet. With the first one we got the best prices ever! To get to Aachen we departed from London Stansted at 7am (far from home, we had to spend the night before at the airport) and costed around 30€ (taxes included). We arrived at Dusseldorf Niederhien (something like that, not the main dusseldorf airport).
But we came back from Maastrich-Aachen airport for 10€ (everything included), the cheapest ticket ever!!!
The main train station (Hauptbahnhof) is in the center of the city, however it does require a little bit of a walk to get to the main sites. It is possible to take the taxi, but we did fine with just walking through the interesting streets of Aachen. Train service is direct from Koln (Cologne), although we came from Welkenraedt in Belgium. Aachen is a border city, therefore it is easy to get to the Netherlands and Belgium from there.
As Aachen has a rather bad parking-policy (there are way to little parkingplaces, scathered throughout town (but definately low costs), one can best go to Aachen by train. It is connecting well to Bonn, Koln and other cities in it's German surroundings, as well as to Maastricht, Heerlen and Geleen (in The Netherlands) and Liege in Belgium.
Our bus network is okay (at all the busstops you´ll find a map of the different lines), however the buses don´t go at night, only until 11.00pm or midnight.
Alternatively take a taxi (stop one or call a taxi company) . Within the center everything lies within walking distance. By car: be careful, in the center you will almost always have to pay for a parking spot!
Nearest airport is: Düsseldorf (from there train S7 will take you to Düsseldorf main train station) - Trains go to Aachen basically via Düsseldorf, Cologne, Heerlen (NL) and Liège (B) - 'Euroline' buses take you hear for a reasonable price from most European countries.
1 hour train ride from Dusseldorf or Cologne. Buses to get around town, you pay I think DM8 for 24 hour anywhere and everywhere AAchen. Make sure you keep your ticket at all times. People just hop in, I wondered why they where not paying, it is because the fare is good for 24 hours. Honor system is practice here. Once you get caught, you can be suspended from not riding the bus at all.
Most of the streets around town is cobblestone, suggest walking with comfortable shoes. Bicycle> bery bumpy!
All trains between Cologne and Brussels stop here so that's my best tip for getting to Aachen. There are also a lot of slower regional trains from Cologne as well as Liege in Belgium.