10 days in Germany in October.

Where should I go?

Wait - take a step back. You've got a return air ticket from Chicago to 'Germany', dated October and you want to make best use of it?

Hard to say, Germany appears so boring to me. Maybe you want to visit the famous "Oktoberfest" in Munich 19.9. - 4.10. or Neuschwanstein or one of these festivals?

http://www.festivalticker.de/festivals-in-deutschland/oktober/

It depends on what you want to see. There are some different landscapes. October might be good for seeing some regions where wine is grown (southwest, Rhine valley), if you like such things. Historically, GDR or Nazi stuff could be interesting (Berlin wall, checkpoint Charlie in Berlin, ummm, there must be more, maybe old Stasi-HQ in Hohenschönhausen/Berlin? - don't know if there's much to see there, though), you also have lots of medieval/early modern castles/chateaux (Neuschwanstein (which is a 19th-century aberration), Heidelberg seems to be popular with American tourists; they also seem to have achieved a high tourist-throughput at "Rothenburg ob der Tauber", which I'd discourage). Don't know, there are different regions. You probably should see Berlin, maybe Hamburg and Munich. I'd say your view will probably be distorted / incomplete if you see the north or the south only.

Best thing to do in Germany is a trip across the border to e.g. France or Italy or Poland or Austria...

I'm flying into Berlin and out of Munich and have nothing planned in between.:'(

Like Elias said, best to do in Germany is to quickly leave it. The same goes for France.

At the festivals: In Germany towns with low numbers are in the north, the higher the number the more in the south they are.

Germany is what keeps Europe from turning into Greece.

If I was still there I'd suggest a trip to Salzburg, it's only a few hours from Munich by train A lot of people from the US travel to Europe only to see the original locations for the filming of Sound of Music, but I doubt you'd be interested in that

But more seriously, if you are in Munich during Oktoberfest, it might be fun going there just to take some pictures of the craziness (you might need to reserve a seat in a tent though a few weeks in advance or they won't let you in, unless you are accompanied by a female).

And I agree with Polybios, if you like medieval towns and castles there will be lots to see. Neuschwanstein is amazing and you get a closeup view of the Alps - but it might be a bit out of the way (there's trains/buses to every village in the entirety of Germany though so you still can get there without a car). And I know someone from the US who just loved Rothenburg ob der Tauber... she keeps telling me about it every month

Also a lot to see in Berlin of course. Köln and Nürnberg are nice places as well. And I guess you probably want to see one of the concentration camps, several Americans told me it was the best thing of their life.

The big towns like Berlin or Paris are grey, thousands of houses, people and cars. I believe it is very similar in many towns.

The difference is the landscape. But in october its rather cold here.

Do you have an idea what you would like to see?

Vienna might be worth a visit, too. You have the old Catholic centre of power there and the old Prostestant (Prussian) centre of power in Berlin. It's a bit remote, though.

I found Dresden interesting. Not because of its nice architecture and the stuff you'd see on postcards, but because of the sight of ruins, some with washed-out signs, which still were a regular part of the 'streetscape' in some areas (like maybe 8 years ago). These still bear witness to 40 years of vibrant communist GDR-economy... ^^ I must admit I haven't been to the "East" often, though.

If you plan to travel with "Deutsche Bahn", the largest railway operator, you should book +3 days in advance, as you'll pay significantly more if you don't. And never expect to arrive on time. October is quite good, though, because neither foreseeable "extreme temperatures" of summer nor winter will add to (or rather provide a cheap excuse for) their utter mismanagement.

Senk ju for träveling wis Deutsche Bahn...

Catholics are evil.

Castles are great.

Definitely will be starting out in Berlin for a few days ... museums and whatever else is near by. And of course ending in Munich. Definitely want to spend time around the Rhine and in the south.

I'm not sure if I want to go up to Hamburg or not. Prefer to minimize traveling.

This could mean "Potsdam": Sanssouci and other Prussian/Hohenzollern stuff.

There is an official website with the "100 most popular travel attractions". It's funny imagining the battle of local politicians each wanting 'their' attraction on that website... Well, I
wouldn't agree with composition nor ranking. ^^ But you could get some inspiration. Having a cursory look, I remembered that I loved the (huge) "German Museum" / "Deutsches Museum" in Munich when I was a kid.

I've often found wikitravel to be quite interesting, as it covers information you wouldn't necessarily find in the typical guides. Didn't check the article on Germany though.