Friedrichshain is one of Berlin's "in" quarters (called "Kiez" here in Berlin) - and still not yet as gentrified as Prenzlauer Berg.
It's an easy place to explore on foot (100 - 2000 m) and most of the older buildings have been (beautifully) restored. At the corner of Boxhanger and Niederbarnimstraße you'll find the "Intimes" movie house (cinema) - the point where Simon-Dach-Strasse begins. This street, with its numerous bars and restaurants is not only popular among German visitors. It leads into side streets where you can find quirky little shops.
On Sundays, "hip" bars and cafes around Simon-Dach-Strasse and Boxhanger Platz compete with each other to offer the best deals for Brunch.
From Frankfurter Tor, take the U-Bahn (subway) Line U5 just 4 stations to Alexanderplatz or in the opposite direction to Lichtenberg, Marzahn and further outwards to Hönow. The tram line M10 takes you left over Warschauer Straße towards Kreuzberg or right, to Prenzlauer Berg. You can reach the Ostbahnhof in 20 minutes on foot or in 5 minutes with Bus #240 from the Grünberger Str./Warschauer Str. stop.