The most convenient way to reach Annaberg by public transport is by train. Annaberg-Buchholz is located on the Zschopau valley railway, a line of the Erzgebirgsbahn, which connects Chemnitz with the Czech town Vejprty just beyong the border. In Chemnitz you connect with the main route Dresden-Nürnberg, a line to Leipzig and other side lines. To continue into the Czech Republic, there are connections in Vejprty. The Zschopau valley railway runs from Chemnitz via Flöha, Erdmannsdorf-Augustusburg, Zschopau, Scharfenstein, Wolkenstein, Annaberg-Buchholz, Cranzahl (where you can change to the narrow-gauge railway to Oberwiesenthal) and ends in Vejprty, a very few trains continue to Chomutov.
Annaberg-Buchholz has three train stations. If you want to reach Annaberg's old town, Unterer Bahnhof (the "lower" station) is the right one. For Buchholz, Haltepunkt Mitte is the closest choice, but there are bus connections from Unterer Bahnhof which might be better than from Mitte.
Unterer Bahnhof must be considered the "main" station of Annaberg-Buchholz. It is not manned, though. A ticket machine is all there is.
Distances to the town centres look short on the map but don't underestimate the walks. The slopes of the valley are steep and the pavement is not friendly to rolling luggage. Better take a bus. The bus stop is a short walk from the station in front of the Netto supermarket in the main road. (In case you need any food or drink, buy it there - the old town of Annaberg has no supermarket.) VMS train tickets to zone Annaberg-Buchholz are also valid on the buses.
Unfortunately, though, the timetables of train and bus do not match well and often the bus is just gone the same minute when the train pulls in. Bad planning.
While train is the way to go TO Annaberg the buses are the prefered transportation for me to get around in the town and surroundings. Since buses and trains are part of the VMS network your ticket is valid in buses AND trains. City buses connect the train stations with the old town/Market square which is a good 10 minutes steep uphill walk from the station Unterer Bahnhof.
Buses that you might want to take are those to Schlettau (to see the castle there) and Oberwiesenthal, the ski town at the foot of Mt. Fichtelberg. Buses run practically every hour or even more frequently. Other buses connect Annaberg-Buchholz with other interesting towns in the Erzgebirge, such as Schwarzenberg, Marienberg, Freiberg.
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Public transportation is the way to go to Annaberg-Buchholz. The trains from/to Chemnitz run hourly (convenient connections from/to Dresden with change in Flöha) and the ride is scenic. These trains of the so called "Erzgebirgsbahn" even run to Vejprty in the Czech Republi where you can catch trains to Chomutov.
(Almost) The whole Erzgebirge mountains are part of the VMS transportation network including trains and buses. Please see their website below for details on fares. They also accept the Saxony ticket and the Schönes-Wochenende-Ticket of the Deutsche Bahn.
When visiting Annaberg please note that you best get off the train at Annaberg-Buchholz Unterer Bahnhof station. From there walk up to the Market Square (steep, about 10 minutes) or catch a city bus (bus stop at the grocery 100 m down the street).
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