GOV. David Paterson hit chic Upper East Side gay club Evolve Thursday night, pressing the flesh and posing for pictures at the Stonewall Democrats’ Christmas party. The festive crowd sipped cocktails and schmoozed — and a few partygoers coyly checked out one of the Gov’s burly and handsome security detail. “There was nothing but praise for the governor,” said one attendee. “I guess his record on gay and lesbian rights sits well with everyone.”