Which place is less expensive?

Definitely Switzerland! Germany is not cheap by any means, but
compared to the Swiss, all other European countries are more reasonable.
Food is probably the most expensive and a simple burger might cost
you between 15 and 20 USD.

On the other hand, Switzerland is a very beautiful and picturesque
country and definitely worth visiting.

One option would be to stay at the Bodensee on the German side,
and make day trips to Switzerland or Austria, as all 3 countries come
border there.

http://www.bodensee-travel.de/angebote/gfx/karte.gif

And here a pictures of some of the towns around Bodensee
http://outdoor-pictures.de/bildarchiv/bodensee/kn.html

Thanks for the input! Would you say that the Swiss cost of living is significantly higher, such that if I were to stay there for four or five days, there would be a noticable difference in my wallet than if I'd stayed in Germany? Or is the difference between a 4-day trip in Switzerland and a 4-day trip in Germany a difference of "only" (!) 100-200 USD?

I do like the idea of staying close enough to the border to visit both places (and Austria too). Part of me wants to say that it's not worth going to a country for just one day, but another part says one day is better than no days!

If you're staying a couple of days in Switzerland, it won't make a huge
difference.

You could fly into Zurich, stay there for a couple of days, travel around,
and when your budget is getting low, drive to Germany and stay there.

Two years ago, I drove through Switzerland while going into Italy.
The gasprices were much higher, and I filled up the tank in Germany
before entering Switzerland, plus we had lunch right after the border in
Italy.

I've been travelling around here and would say Austria is the best value of the three; but CJ is right about seeing all of them! If you're hiring a car, no problem to go from one to the other. Distances aren't great.

I wasn't planning to do any driving; I'll be limited to foot and train. It's one reason why I was going to restrict myself to just one or two cities. We'll see...

Go to the Lake of Constance (Bodensee) - there, you can easily not only visit all three countries by train but by ship, too.

(Looking at the [official] statistics and regarding my personal experiences [with the EURO it's quite easy :wink: ] as well as those of the Austrian in-laws, Germany is in the whole cheaper than Austria.)

Have you checked All Europe Rail?

http://www.alleuroperail.com/eurail_index.php?passID=15

I've looked at a number of similar deals--Eurail, EuroRail--and have been wondering about it. Some friends of mine have had lukewarm things to say about it. The general concensus among them is that it doesn't save me a whole lot of money (I could just buy tickets the normal way), but does have the "slight" advantage of not making me wait in ticket lines. Any input?

My kids and their friends used Inter Rail when they travelled through Europe.
They saved around 50% of the normal train tickets.
As they were young they used the night trains to save on hotels, too. :wink:

It actually depends - how far you want to go when, ffor instance.

Some tickets (I know that only for Germany) might be got online and "last minute" cheaper.
But generally spoken, those 'combined tickets' are an advantage.

Thanks for your help, everyone. I decided to go to Switzerland... I'm off to Zürich in about a week for just a few days. I may or may not visit a few other nearby cities while I'm there, depending on my money situation; either way, I'm sure I'll have a great time.

You will! It's a terrific country, and much cheaper than it used to be 10 years ago.
Have a wonderful time!