Yeah well near Aachen there is the Three Country Corner (Dreilaendereck), it is a hill outside of Aachen where you could stand in all 3 countries at the same time. There is a place to eat and a tower up there if you wanted to go.
Yeah, there where you are going in the middle of town is the Dom (Cathedral), there are small alleys and cobblestone streets there. If you walk for like 10 minutes you can get to the Ponttor (Pont Gate) which is a part of the old city wall, it is pretty interesting and worth looking at if you are already there. Also as I said its on the way to food
Right around Aachen there isnt much to be honest. Vaals in the Netherlands has a small palace, but it isnt much to see. You can go to a grocery store in Vaals, it is cheaper and you can buy things in cans, which is nice if you just want to take drinks in a backpack and not have to lug around 1.5L bottles like in Germany. Also drinks in the Netherlands dont have a deposit, like in Germany. In Germany, on all cans and bottles there is a 25 cent deposit. I would advise buying things in the Netherlands or in a grocery store.
Another thing to do in the Netherlands is to buy fuel for your car, particularly if its diesel. When we lived in Aachen we would drive to Vaals to fill up.
Be careful with the parking garages here, they are really small and tight and watch out for the roof if you open a trunk, as the clearance is also low.
I guess one last thing, if you dont want to go to the Pontstrasse to eat, you could eat right near the Cathedral. The city hall also looks like a church, but it isnt, its the one with two towers facing the Marktplatz. On a corner there is a restaurant/bar that has windows made like they used to do with circles of glass built together to form window panes, I believe it is called Post or something. Anyhow you could eat there, or to the left of it at the Haxenhaus which was formerly the potato place, my wife and I ate at both of them, honestly I cant say that anywhere we ate in Aachen was particularly good, but I wish you the best of luck!
[This message has been edited by Randy03 (edited 4/6/2011 5:39p).]