There's Kaizuka which is Japanese/Sushi on Culver between the Starbucks and Santa Maria BBQ. Wilson is also new but it's not in downtown CC, it's just past the Helms Bakery complex on Washington. The only other new restaurant I can think of is Cafe Ugo, the "Italian" joint on Cardiff.
Are you thinking of Wilson's in the MODAA Building on Washington, somewhat east of "downtown" Culver City?
Or Beacon (which is not all that new anymore), near the Helms Bakery Building on Washington.
You *could* walk to the movie from either of these but it would be probably almost a mile, as opposed to blocks from either Ford's or Tender Greens. Other places closer to the theatre, would be Bistro de la Hermitage (french), Kaizuka (decent Japanese) or Double Dutch Dinette (a menagerie of cuisine, sort of like the old Menagerie, as a matter of fact).