Bearpit Karaoke

Rapidly becoming a Berlin institution, every Sunday afternoon thousands of people make their way to Prenzlauer Berg's Mauerpark (literally Wall Park), which is on the site of the former death strip between East and West. There's a very popular flea market and numerous food stalls, but the real highlight takes place in the amphitheatre from 3pm. Then, an affable Irish chap calling himself Joe Hatchiban pedals up with his mobile sound system and declares Bearpit Karaoke open for business. Anyone can sing, though Joe has a veto if he doesn't like your song choice. There is a regular cast of characters who hog the mike, including a wildly bearded man called Detlef who always sings My Way in German and shuffles on the stage carrying load of carrier bags. It's a gladiatorial atmosphere, not for fainthearted singers. If the crowd love you, they will sing and cheer along and you'll feel like a star; if they think you're rubbish, prepare to be booed.
• bearpitkaraoke.com

Tempelhofer Park

Until recently, this was a functioning airport, most famous for the starring role it played in the Berlin Airlift of 1948-1949. The runway is still there; so is an air traffic control tower and even a few planes frozen in time at the departure gates. The terminal building, constructed to Hermann Göring's exacting standards in classic Nazi architectural style, is in perfect nick, though it's out of bounds to the public. After much argument over what to do with the land when the airport shut in 2008, it finally reopened as a park in 2010. In clement weather, the grounds turn into Berlin's sportiest spot. Triathletes jostle for space on the air strip with rollerbladers and skateboarders; a softball game always seems to be in full swing and there is inevitably a football match to gatecrash. It's popular with picnickers too, though there is next to no shade on a sunny day.
• tempelhofer-park.de

Spreepark deserted funfair

One of east Berlin's more off-beat attractions, the Spreepark was once the only amusement park in the GDR but was left to rot in 2002 after a scandal involving 180kg of cocaine hidden in the Magic Carpet Ride (it's a long story). It's a magical, if ramshackle, place – frogs now colonise the logflume; the mouth of the rollercoaster is sprouting foliage and the ferris wheel stands perfectly intact. For a long time the funfair was out of bounds, though popular after dark with urban explorers and local teenagers out for an adventure. Recently, the owners started running legal tours each weekend. They are usually in German only, though even monoglots will enjoy nosying around without understanding a word. Sometimes your guide is Sabrina Witte, the colourful daughter of the disgraced former owner, who gives a no-holds-barred account of where things all went wrong.
• To book a tour see berliner-spreepark.de

Soviet War Memorial in Treptower Park

When the iron curtain fell, one condition of German reunification was that all memorials to the Soviet dead would be maintained. This enormous site, just east of where the Berlin Wall once stood, is perhaps the most gobsmacking of all shrines to the Russian dead. Designed by the Soviet architect Yakov Belopolsky to commemorate 5,000 of the 80,000 Soviet soldiers who fell in the Battle of Berlin in April-May 1945, the memorial also doubles up as a cemetery for the dead soldiers. The star of the show is the 12-metre tall statue of a Red Army soldier with a sword holding a German child, standing over a broken swastika.

Teufelsberg

Situated on one of Berlin's rare hills, the Teufelsberg – literally devil's hill – can be seen for miles around, largely thanks to the five radar domes plonked on the top. During the cold war the Allies ran a sophisticated listening station on the site, eavesdropping on what was going on in the East. Since the Wall fell, the set has been left to ruin and the Berlin senate has still not decided what to do with this prime bit of real estate. In 2007 there was a scandal after film-maker David Lynch mooted the idea of building a university dedicated to Transcendental Meditation on the top. Like the Spreepark, until recently it was considered trespassing to explore the dilapidated Teufelsberg complex. Now there are legal tours run every Sunday at 1.30pm from Berlin SightOut.
• Tours in English cost €15. Call +49 163 858 5096, berlinsightout.de

Memorial to the Murdered Jews of Europe

Opinion is divided on the success of Peter Eisenman's holocaust memorial, which consists of a 19,000 square metres (4.7 acres) site covered with 2,711 concrete slabs or "stelae", arranged in a grid pattern on a sloping field. Some find the site moving; others are distracted by the number of tourists who consider the smaller slabs the perfect spot to sit and eat a sandwich while their children play hide and seek. Whatever you think of the design, don't miss the incredibly moving information centre underneath, which, among other fascinating exhibits, lists the names of all known Jewish Holocaust victims.
• stiftung-denkmal.de. The information centre is open every day except Mondays from April to September from 10am-8pm and from October to March from 10am-7pm

MountMitte

There are lots of good places to climb in Berlin, but MountMitte is the most fun – especially for children. It's an aerial adventure garden, like an urban GoApe. There is lots to explore in this surreal complex, where real Trabant cars are suspended in the air and canoes seem to be flying. You wear a climbing harness and are attached to the vertiginous rope course so you can't fall off. Climbers must be at least 130cm tall to take part.
• Caroline-Michaelis-Strasse 8, +49 30 555 77 8922, mountmitte.de. Adults €19, students €17, 14-17-year-olds €17, children €14. Open Mon-Fri from 2pm; Sat-Sun from 10am. Last admission two hours before it gets dark

Strandbad Grünau

Possibly the most charming of Berlin's many lovely lake beaches, the Strandbad Grünau is tucked away in deepest east Berlin. But it's well worth the journey. Unlike the more popular Strandbad Wannsee in the posher west, the water here is deep enough for proper swimming and it doesn't get quite as horrendously busy on a hot summer's day. There are striped Strandkörbe (beach baskets) to hire as an alternative to a boring old deckchair and a decent cafe too. Those so inclined can go nude in the secluded area marked FKK.
• strandbad-grünau.de, admission €5/3; €10 for a family ticket (two adults and one child with €2.50 for every subsequent child). Open May-September from 10am-6pm (7pm in the school holidays)

Canoeing Berlin

Despite being landlocked, Berlin is a pretty watery place, with the River Spree and the Landwehrkanal winding through town on their way to the city's many lakes. If you hire a canoe from Kajak und Kanuverleih Kommrum, they deliver the boats to your desired starting point and collect them again from wherever you end up. A particularly enjoyable day would take in either Wannsee lake in the west or the Müggelsee in the east.
• Schnackenburgstrasse 4, +49 30 8507 8734, bei-anruf-boot.de. Daily price per boat (minimum four boats) starting from €21, guided tours per boat (minimum five boats) starting from €30

Freiluftkino (Open air cinema)

Enjoying a film alfresco is a great summer tradition in Berlin. There are a number of parks and gardens where you can give it a go. The one most likely to be showing an English language film is the Freiluftkino Kreuzberg, which is in the back garden of the 3Schwestern restaurant in the old Kunsthaus Bethanian arts centre. Chairs are provided, though you might want to bring a blanket and a waterproof – just in case. The show goes on whatever the weather.
• In the yard of the Kunstquartier Bethanien, entrance opposite Adalbertstrasse 73, Mariannenplatz, freiluftkino-kreuzberg.de. Tickets (€6.50) go on sale 30 minutes before the performance

• Helen Pidd is the Guardian's Berlin correspondent