The sound stages at CBS studios were the main location for Remington Steele. Permanent sets were erected on stages 4,5 and 6 for the interiors for the office, Laura's house and loft, and Steele's Apartment.  Of course they are long gone but the show often left the confines of the small backlot to go to various locations around the city of Los Angeles. It has become an addictive game of mine to watch the show and see if I can't track down locations using the best invention since the internet: Google street view.  Why?   I don't know, but it's kind of entertaining and challenging to see if I can find enough little clues to solve a tiny mystery.  Some of these are from the dvds as well but there are a lot I don't have, if you know of any please email the shrine.

CBS Studio Center  4024 Radford Ave. Studio City (closed to the public but you can get pretty good views just driving by.) Here is an awesome interactive map. Alias Radford Studios, and way back when, was Republic Pictures.

Multiple episodes featured the front gate of the studios (alias Central Hollywood Studios on the show) including:

Steele Spawning, Red Holt Steele, Stronger than Steele

The Administrations Building just inside CBS Studio Center to the left of the main gate, was used as the parking lot for Steele Investigations in various episodes including:

Steele Belted, Vintage Steele, Steele in Circulation, Love Among the Steele, Elementary Steele (mental hospital) , Steele on the Air (Radio Station), Steele Blushing, etc.

 

Remington Steele Investigations 2053 Century Park East, Los Angeles  This is in the Century City area of the city.

 

I think for the 5th season the permanent sets of the Steele offices and Remington's apartment were moved/rebuilt(?) to the soundstages at 20343 Ave Crocker, Valencia, Santa Clarita, CA I don't know who owns/owned those stages, possibly Paramount. 

Here are the locations broken down by episode and season:

Locations:

Season 1  Season 2  

Season 3 Season 4      Season 5

Here are the locations mapped broken down by areas of Los Angeles:

Maps:

Studio City Area      East/Pasadena     United Kingdom

West and South        Central