The best way to get around the heart of the city (the old town area) is by walking. There are taxis to be found, but most places of interest, hotels, and restaurants are within a 10-15 minute walk of each other. Further away, but still walkable from the old town area is the train station.

Buses -- There are local buses as well, but if you aren't well versed in German that could be a challenge.  However, this is a very economical way to get around. You might even consider taking the bus to the Zentralklinik from Weimar or even from the Klinik to Weimar. The one way cost is 2.4 Euros, a real deal compared to taking a taxi.

Taking a bus from the Zentralklinik -- A bus leaves the Klinik at about 8 minutes after every hour. Buses start running from the Klinik at 8am and stop around 5pm.  Take Bus #223 to Bad Berka. This bus goes to the Bad Berka train station, the train station you transfer to Bus #221 which will take you to the Weimar Hauptbahnhof (train station). This is about a 35 minute total ride.  For exact times please see DB Bhan website and use Zentralklinik, Bad Berka as a starting point and Weimar as an end point.

Car Rental -Some patients have rented a car in Frankfurt, and driven to Weimar. The experience with Enterprise, through Expedia has worked well. For navigation, some people have purchased the Tom Tom XXL 540TM World Traveler, which has US and European maps. It is small convenient for travel, even has traffic in both the USA and Europe.