If you choose the hostel, rent out one of their bikes for the day (if not, there are plenty other rental services throughout town). Since it's Tuesday, start off going to the Turkish Market, where you can spend a peaceful hour wandering along the Landwehrkanal, listening to the buskers, and packing away some sandwiches or other portable foods for the day's journeying.
Grab a quick espresso at Companion Coffee and go to Kisch & Co. Buchhandlung next door, where you can inquire after a map of the city and, most importantly, the Grunewald.
Bike further south to Tempelhoferfeld, and make a couple rounds of this glorious runway-turned-recreational field before heading further West to the Grunewald. Here, equipped with your map and the help of the (somewhat befuddling) path markings, lock your bike somewhere safe and begin exploring on foot this incredible green region just outside of the city.
Grab a bite to eat at the scenic Krumme Lanke, Schlachtensee, or the much smaller Teufelsee. If you are game, take a dip or sunbathe nude among the FKK enthusiasts after lunch.
Take a path to the Havel, the Spree's much bigger sibling. If you don't mind walking back through the forest after dark, stay for a stunning sunset.
Otherwise, make your way back before dusk and, as the day turns to night, grab a beer and a hearty, healthy meal at Prinzessengarten in Kreuzberg. Stretch your legs under the classically German pine-and-metal communal tables before biking one last stretch to the hostel to crash for the night.