I wouldn't consider any of the restaurants recommended quiet & relaxing, let alone good food. For what you asked for, Le Valluris is probably the best - very romantic on the patio, relaxing both inside & out. Excellent food & wine list - try the whitefish in dijon champagne sauce.
Great recommendations from ajandjulie , give Kaiser Grill a go at happy hour best bar menu in town , Grill a Burger across the street from Kaiser a few blocks north great juicy burgers with full bar outside patio . Zin Cafe French touch but very reasonable, Spenser's at the Mountain lunch / dinner upscale classy end of Taquithz Canyon by the PS museum. Lobster House as far as I know has closed.
In Rancho Mirage on Hwy 111 a Cheesecake Factory has opened at the River a open air walking / shopping area also a PF Changs is located within that complex.Both have outside patios if its not to hot .
Further down hwy 111 into Palm Desert as mentioned by ajandjulie cruise on down to El Paseo strech your legs walk 7-8 on one side of the street cross over walk back. Yes, cafe mentioned in above post very relaxing outside patio. Mexican if interrested Armondo's also on El Paseo. Above Sack's is a Tommy Bahamas island type of fare and Pacifica's seafood and steaks a bit upscale but casual.
Let's not forget on Thursday nights Palm Canyon is closed to cars Village Fest is a happening venue plenty of street food and stuff to buy. Enjoy our desert --- desertguy
We're going to the Palm Springs area in October and it is one of our favorite places to visit. In Palm Springs itself there are many places right on the main road S. Palm Canyon Dr. that are good. Two that standout in my opinion are Las Casuelas Terraza a mexican place with a great patio area. The other is Kaiser Grill. Both places I've only had lunch. Another lunch spot was a place that I had lobster. Lobster might be in the name but I'm not sure. Something like the lobster hut maybe.
Just a short drive from Palm Spings on the 111 is Palm Desert and El Paseo a street with lots of art galleries and restaurants. I would highly recommend the Cafe Des Baux Arts. I've had breakfast, lunch and dinner there. We liked it so much we got to know the owner by the end of the week we were there.
The 111 corridor has lots of really good places to eat. There's a Roy's which was spectacular and there's a place called Halawea Joe's which is very good.
I'm looking forward to our trip and all the great food.