The farthest I traveled was to Koblenz, which is about 50 miles away from Mainz. I got there by taking a bus to Wiesbaden, a city right next to Mainz, and a train from Wiesbaden to Koblenz.
Since I've been in Europe (I arrived in early September), I've visited 6 countries (Germany, France, Austria, Slovakia, Hungary, and the United Kingdom). Within Germany, I've visited Koblenz, Wiesbaden, Frankfurt, Cologne, Saarbrücken, and Berlin.
I got around on foot, by bike, by train, by bus, and by trolley.
The most interesting place I visited was the monument Deutsches Eck (German Corner) in Koblenz. This is where the Rhine and Moselle rivers intersect. Here, there is a statue of Kaiser (which means "emperor") Wilhelm I. He was the first emperor of Germany when it united in 1871. I was able to climb up to the top of the pedestal of the statue, which has a beautiful view of the two rivers.