There's a place called Rouge et Blanc on Grant [btwn Sutter & Bush]. It's physically a nice space, but I've only been there for private events, so can't attest to the choices, or expertise of the staff.
You might do better in the long run at a restaurant with a good wine list. Wines by the glass are readily available at most establishments. Barbacco in the Financial District comes to mind as a place with extensicve wine choices. It's walkable from Union Square, although maybe not as low key as you might want.