Maybe I've seen too many pictures of '50s and '60s motels (only kidding), because this one looked very familiar. However, a quick search didn't turn up any previous mentions.
The Kent Inn Motel was at 920 S Figueroa Street. The seller dates this postcard as 1960s.
eBay
I also found this daytime shot.
www.cardcow.com
The listing below is from the 1970 Hotel & Motel Red Book.
archive.org
I've checked Historic Aerials, and it looks like the building was still there in 1989 (it's listed in the 1987 CD), but there was a parking lot there by the 1994. Since 2009, the site has been home to these apartments which bill themselves as "APEX. The One." I'm not a fan of these modern designs where a section gets pushed out of line just because they can.
GSV