If you have just light dust, the Chevron on colemon (where In-n-Out burger is) has a completely touchless option. Uses only chemicals to wash the car that works well enough. If you have any debris stuck to the car, it won't work that well.
I've used Bubbles in Sunnyvale (all hand wash) and Classic Car Wash in San Jose. Note - for Classic ask for a hand wash, which is slightly more expensive and takes a little longer. They don't run the car through the tunnel with a hand wash. Both did a fine job.
+1. As a result of the water conservation measures enacted in my city a few years ago, it's no longer ok to do a traditional wash in the driveway with a hose and bucket [see footnote below], so I learned how to keep the car clean without ever leaving the garage. I just use spray bottles filled with water, some vinegar-based Windex for the glass and tough spots, and a stack of clean microfiber towels to gently mop away the dirt after spray-soaking the surface. I'm extra careful about keeping a light touch to avoid swirls/scratches. Works great and there's no waste water to run off into the drain.
[*] I looked up our municipal code online. The wording apparently has a loophole that permits washing a vehicle if "the hose is fitted with a shut-off nozzle or device that causes it to cease dispensing water immediately when not in use." Still, I doubt I'll ever go back to that old method.
Edit: this comment may or may not be helpful, as the thread is specifically asking for recommendations on where to have your car washed by someone else. Sorry about that.
I use Optimum No-Rinse, it takes very little water, and works fantastic (so no hose in the driveway). If I end up getting really dirty (after a rain perhaps) I can use my power washer quickly to knock off the heavy stuff, then pull into the garage and use the ONR. Overall uses very little water. I just installed a water filtration system as well (on a 'switch') that lets me use soft water for the wash.
Try it out! Much safer than just using water, scratch free washing! I keep the mixture in a spray bottle, and also use a small bucket of it when I do the wash. I also have "The Big Red Sponge".