If you are visiting during the winter months, visit Peristal Singum a surreal underground labyrinth experience.
Take the Free Tour that starts at the Starbucks near Brandenburg Gate
and lasts for 3.5 hours. Yes. It is free. No hidden fees, just tips if you want to and it is amazingly awesome!
You'll probably find this out if you search enough but Mauerpark becomes a flea market on Sundays and Hackescher Markt is a great place to buy handmade souvenirs on Thursdays or just people-watch and sip coffee on other days.
Do not miss the park next to the Wasserturm where you will find a trampoline built into the ground, free to use and a Table Tennis spot out in the open!
If you're a foodie take the Evening & Food tour by Fat Tire Bike Tours.
Walk around, explore the city. The city itself is like a person you would like to hang out with. One of the most memorable things I remember seeing while walking around is two neon signs playing Rock-Paper-Scissors atop the Oberbaumbrücke, a beautiful bridge which is adjacent to the spot where the East Side Gallery begins.
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