There actually is touristy stuff to see near Radio City - Rockefeller Center is right there, so you can check out the Christmas Tree and the Ice Skaters... St Patrick's Cathedral is right there, and a branch of Magnolia Cupcakes. If you walk 15 blocks south, you're at Macy's and can check out the holiday window displays if you're so inclined. 10 blocks north, and you're in Central Park.
Keen's Steakhouse is near Macy's. I've never been there, but I think it's an old-school NYC steakhouse, and not a tourist trap. If you're into tourist traps, I think Guy Fieri's restaurant is pretty close to Radio City.