Public. Not exactly the name you’d choose for a restaurant that’s all about intimacy and hominess. Nevertheless, that’s the theme of NoLIta’s newest eatery, which opens today for lunch (Friday for dinner). Brought to you by acclaimed chefs Peter Gordon, Anne Hansen, and Brad Farmerie, who’ve created a spot that’s cozy and refined. The interior is somewhat denlike — mahogany paneling and an alcove filled with books — yet coolly industrial/minimalist, thanks to lofty ceilings, sleek track lighting, and modest tables and chairs. But somehow the mishmash of urban and down-home charms works brilliantly. The menu features dishes like grilled New Zealand venison with fennel, pomegranate, and truffle dressing, as well as sea bass with saffron new potatoes. Add in the array of superb wines, a private back room with fireplace and couches, an atrium-like bar area, and the individually wrapped take-away soaps (instead of matches) in the restrooms, and it all adds up to cozy warmth and stylish elegance — a great combination. Not to mention a rare one. Public, 210 Elizabeth Street, between Prince and Spring Streets (212-343-7011).