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Photo: Erika Rathje, CC BY-SA 4.0 via Wikimedia Commons
The "Dechsi" as it is frequently called has in the past had problems with algal blooms and was famously immortalised in an absurdist song by local band J.B.O. purporting the existence of a Great White Shark in said body of water. The Algal blooms were fixed through extensive redesigns of the lake, including routing one of its tributaries around it, but you can see maintenance work done on some of those installations from time to time. The Dechsi is frequently the site of events like "Rock am See" or "Klassik am See". Even when swimming is not possible, you can rent boats of various kinds or simply jogg around the lake.
© OpenStreetMap contributors
bouldering hall
A bouldering hall in Dechsendorf, a somewhat outlying suburb.
At Entlas Keller (the duck's cellar), you can visit the extensive underground paths and former beer storage areas. Before artificial cooling was invented, people dug cellars into the hills and brought ice in there to cool the beer throughout the year; at this place you can visit Erlangen's extensive underground.
The water tower on the Burgberg hill was built to store the city's drinking water supply and can be seen from many locations within the city. It was built in 1904/05 and is still in use.
You probably would not expect to find much in Bubenreuth, a rather small town just north of Erlangen's Burgberg. However, this Franconian town is home to great music and instrument makers. This museum is located in the town hall and has been initiated by a local association. It shows the local string instrument maker history (which most significantly relates to makers of violins), which is rich in the 20th century, after World War II. While not part of Erlangen, it's no farther than the south of the city.
Berch
Begun in 1755, this festival is held every Pentecost (Whitsuntide - seven weeks after Easter) for 12 days every year. The first day is always the Thursday before the Pentecost weekend. Similar to Oktoberfest, but more German owing to the absence of tourists. The festival draws crowds around the 1 million mark, so hotels might get crowded and overpriced during this time of the year. At 23:00 the main action stops and the party crowd goes on to the various discos and bars that keep going until 05:00.