You will be in Berlin for Christopher Street Day (Gay Pride) so the gay scene will be pretty lively more so than usual.
Behind Hackescher Markt is The Liberate which tries to be one of the swankier places in Mitte...across the street was a dear friend's bar The Sharon Stonewall which has since closed. Schöneberg is the "older" gay area (think The Castro or Christopher St NYC) where you can also find the dirtier sex clubs and fetish parties.
I would suggest just popping into any of the gay bars you may be around the first night you are there and you can pick up a copy of BLU which usually has the whole month's party listings and adverts for gay friendly businesses.
While not gay owned/operated but places I favor to eat include Alpenstueck, Dos Palios and Dudu.