I will be living in Aachen for a year and I love to travel. In my home country Australia i would often do weekend getaways by car. However I do not have a car here. Europe is incredable and I want to make the most of my time here.

What are some ideas for cheap weekend trips I can do from Aachen?

So far I have been for trips to:
Amsterdam
Brussels/Bruges
Cologne
Dusseldorf
Paris
London

Are there any beautiful places you would suggest?

The two obvious are Liege and Maastricht. Liege is a slumbering old town with a beautiful modern railway station and Cathedral. Maastricht is a smaller, managable ancient city with expensive shopping streets as well as the usual dope pubs and crazy coffee houses (or is that the other way around) it also has a lovely railway station.

Further afield there is Trier/Luxembourg city, the whole of the Mosel valley (famous for wine, walking and cycling) follow my name back for a few ideas of what to do.

All these are within a reasonable commute from Aachen (but don't mention the Belgian nuclear industry)

Maastricht is lovely and nearby.

Gent, Antwerp are neat cities - the Rhine Gorge by Koblenz (take K-D boats - www.k-d.com) - for ideas by train check www.budgeteuropetravel.com (online European Planning & Rail Guide gives many options in that area by rail); www.ricksteves.com

And yes Mosel - take train to Cochem - base there and see the gorgeous Mosel.

Before Christma be sure to check out famous Christmas Markets like those in Frankfurt, a nice enough city too to spend a weekend in.

Maastricht is lovely and nearby.>

Yes was surprised at now nice Maastricht was - unique look from other regional Dutch towns. Maybe combine with Liege?

Tiny Monschau and Prüm are two villages close to the Belgian / Luxembourg border that are quite pretty.

For Monschau there is a bus from Aachen and for Prüm you will need two trains, a bus and a spare three hours.

Lavandula

Should also be Oktoberfests in little and big towns all over and wine fests also on Mosel and Rhine.

And Munich is about 5 hours by train I think - leave early one day, return late the next Oktoberfest is awesome even if not drinking beer.

You have unfortunately missed most of the big wine festivals on the Rhine for this year but in Boppard on 30 September there is a fireworks display on the Rhine and a wine fest from the Friday till the Sunday.

http://www.weinfeste-online.de/index.html

(a very chaotic list of festivals for 2017 and 2018; the English version is all about Rhine cruises and not the list of festivals so I would struggle through with the German and use Google Translate if necessary).

You can still visit the wine-growing regions on the Rhine (particularly those in Rheinhessen and the Rheingau) as it's a very nice time to visit, being soon after the harvest. Everywhere there will be tastings and light meals available to accompany the new wine (visit the 'Strausswirtschaften', or temporary pubs).

Lavandula