Submitted by Jonathan -
This is a similar, more colorful, "coffee cup" sign from Lester's Diner in Bryan, Ohio. The similarities of this sign and the one shown in the opening credits of ALICE are remarkable.
UPDATE: Mel's Diner in Phoenix originally opened in 1963 under the name Lester's Diner, named for it's owner Lester Bammesberg. This is the same owner as the restuarants in both Bryan, OH and Fort Lauderdale, FL. This explains the similarities, as Mel's was a takeoff of the original Lester's.
Coffee Cup sign from Lester's Diner in Ohio.
Lester's Coffee Cup sign from Florida