Los Angeles airport
 

Is there a restaurant in the LA airport or within a short taxi ride where one can have a nice dinner? (Not fast food)

There is a very nice restaurant called Barnabey's in Manhattan Beach that is only 2.5 miles south of the airport at the corner of Rosecrans and Sepulveda. It is part of a very small hotel. Good atmosphere and food. At LA Airport there is the Theme Building (kind of a Jetson's looking building) that has a restaurant. I've never eaten there but I have heard the food is okay but expensive. Maybe Sam Hemphill knows? ;)

Take a short cab ride to the Ritz-Carlton in Marina-del-Rey and have a glorious meal at The Grille!

Also in Marina Del Rey is the Cafe Del Rey, just down from the Ritz Carlton. They serve the best crabcakes with pink grapefruit sauce! Very close to LAX. Wouldn't recommend the restaurant at the airport.

Try the restaurant at the LAX Wyndham Hotel. I can't remember the name, but we've always had very good meals there. It's actually within walking distance of LAX, but you can also call for their courtesy shuttle.