There was a joke once that Berlin-Wedding is the new hot place to be in Berlin. That joke is like 30 years old but the time may have actually come that Wedding is the new trendy area in Berlin. Wedding has many old buildings with nice flats and is well connected via the metro line U8.
There are some parts of Lichtenberg close to Friedrichshain. Check out Lichtenberg in case you can't afford Friedrichshain but still want to live close to the party.
Some find Tempelhof boring and this might be the case but some parts of it are close to the Tempelhofer Feld. The former airport now turned park has many outdoor options like skateboarding, softball, beach volley ball, a barbecue area and public urban gardens and is teaming with life during the summer.