Chop House is one of the Top 10 steakhouses in the US (I have read) - fabulous! Sammy G's is another that is more continental/Italian in flavor. Copley's is another one - was originally Cary Grant's desert home. From the other response, Cheeky's is just breakfast and lunch starts at 11:30 - they are closed Tuesday - close each day at 2 pm - very unique and tasty items... The Falls Steakhouse is another good choice, as well as Matchbox. Down below Matchbox is my favorite: Maracas (formerly Mariposa).
All of these mentioned are on Palm Canyon in either uptown or downtown Palm Springs and are my favorites (I live in Palm Springs, so I frequent all).