The Fichtelgebirge - a hilly region rather than the mountain range the German translation suggests - make an interesting excursion for a day trip from Bayreuth. They form the shape of a horseshoe with the open end towards the nearby Czech border.
Lying to the northeast of Bayreuth, they are probably easiest reached along the valley of the Weisser Main river. The road heads up to Bad Berneck and two of the highest peaks in the northern part of Bavaria. From there it winds through hills to Bischofsgrün, another 'Kur' resort. (German towns with the 'Kur' designation usually have a healthy tourism aspect to them such as mineral springs or particularly clean air.)
The town of Wunsiedel and its rock formations makes a good stop along the B303 and this route eventually ends in the larger town of Marktredwitz. A loop back to Bayreuth can be taken through the southern leg of the horseshoe down towards Kemnath and then to the east. Alternatively, the northern edge of the mountain range can be explored by heading up to Selb, famous for its porcelain, and then south-east along the country roads.
Surrounded by seven hills, Bad Berneck is an attractive resort town of 2000 inhabitants with a historic centre on the former Via Imperialis trade route. Nowadays, as the 'Bad' suggests, it is a spa resort specialising in Kneipp therapy. Plenty of walkers choose Bad Berneck as a base for hiking breaks, with good access to the longer Fichtel mountain trails or to the routes up the Ölschnitz valley.
Bischofsgrün, nestling between the two peaks of the Schneeberg and the Ochsenkopf, is on the route between the lowlands and the former mountain mining villages further to the east. The important tourist industry developed with the arrival of the train line and was helped with the designation of the town as a 'Luftkurort' in the 1990s - an official designation meaning a health resort with particularly good air quality.
Town website: 
Wunsiedel is a larger town of just under 10,000 inhabitants which serves as one of the centres for the Fichtelgebirge region.
It is famous for its rock labyrinth to the south of the town. One of the first visitors here was famous German writer Goethe and the Luisenberg Labyrinth is named after a popular Prussian queen of the 18th century. The interesting and scenic circular route through the granite formations can be undertaken with decent footwear and is very popular in the high season in summer. The neighbouring stage at the bottom is the location of the annual Luisenberg Festival, the oldest open-air festival stage in Germany.
Wunsiedel also houses the Fichtelgebirge museum, a display of regional history which concentrates on the geology of the area and the mining industry around the town.
Town website: 
Marktredwitz is one of the larger towns in the area with a population of around 17000 inhabitants. It was originally part of the Austro-Hungarian Empire, belonging to the town of Cheb over the border in what is now the Czech Republic. It became part of Bavaria in a swap for the town of Vils near Reutte after the Napoleonic wars. The town houses the Egerland Museum, which concentrates on the history and culture of the German-speaking population of the Egerland around Cheb.