I've heard about some manicurists offering to clean your rings while you have a manicure. On the rare occasion I ever had a mani at a spa or salon, I always removed my jewelry before going...and if I hadn't, I don't think I would want to hand over my rings. However, I do like to have my rings cleaned so I just do it myself at home.
I have an electric sonic jewelry cleaner (made by Salton - it's ancient) and it works very well. I simply add my rings to the basket and submerge it in the cleaning solution in the unit. I turn it on for a few minutes and then gently brush in between the prongs and settings to remove any dirt. I rinse the rings after I put them back on in warm water and just dry my hands. I've got a terrible fear of losing my jewelry down the drain so I always pull the drain plugs up before I start this cleaning process and I don't go anywhere near the sinks! It definitely makes diamonds sparkle and gold gleam. Always follow the directions included with jewelry cleaning solution or sonic cleaners - they are not safe with all jewelry (eg. pearls, opals). I've re-used the same solution over and over but should probably go get a new bottle. It's just one of those things I always forget to pick up...and DH has come to learn it's just better if I stay out of jewelry stores all together!
You can find ultrasonic cleaners for at-home use on-line, at jewelry stores, or discount stores. They are not very expensive (about $30) and, like I said, I've had mine for years (and it was my mother's before that!). If you have nice jewelry it is worth the small investment to keep it looking clean and shiny.