Hi Laura,
Mittenwald has one train station. It's a very easy 5 minute or so walk from the station to the pedestrian zone. Mittenwald is not big and is not a city. It is a gorgeous Bavarian village surrounded by Alps. Simply beautiful!
The cable car in Mittenwald is called the Karwendelbahn. Although it does not share a border with Austria, it's a great trip.
www.mittenwald.de/index.shtml?en_m_karwendelbahn
What you are thinking of is the Zugspitze, which you can get to from Garmisch (20 minutes from Mittenwald). From the top of the Zugspitze, you can walk back and forth over the German/Austria border.
www.zugspitze.de
Seefeld, Austria is about 20 minutes (by car) south of Mittenwald and Garmisch is about 20 minutes (by car) north of Mittenwald. Out of the 3, Mittenwald is best (IMO).
Hope this helps.
Paul