Hello:
My wife and I have been doing ballroom dancing for 30 years and tried most of the cruise ships that come to our town (San Diego) If we want to take a cruise from the East Coast, then Royal Caribbean has started to advertise that they are now offering Dancing at Sea cruises from Fort Lauderdale, Florida.
They seem to have a brass orchestra (brass is not generally good for ballroom dancing, particularly when it replaces wind/string instruments. If it is used with mutes or only occasionally, it is tolerable. But we don't like Royal Caribbean food, service, and care of passengers in general. The best cruise lines we found, 5 stars, are Holland-American. Cunard ships are good too, but expensive and only sail across the Atlantic to English or formerly English ports.
Holland American has some two or three member groups, who play some requests, but only of voyages of 14 days or more. There are also clubs, like "Dancers at Sea" and a few others, but they seem to want people,[who can probably dance better than they can] to take lessons from them on the ship. On the Holland American ship "Zaandam" they provided a DJ who only had hip-hop music and no dance floor. Not appropriate for older people (over 20.
I was so disgusted with the Bryant club from Phoenix that I flew home from Mexico as soon as the ship docked.
We took Princess Sapphire to Alaska from Seattle and they had the "Dancers at Sea" club giving lessons on the dance floor. They provide partners if you are single and want to dance. It was tolerable but not good. Brassy and no requests.
The best cruiselines for ballroom dancing, with a good uncrowded dance floor, and without noisy brass, we discovered is the Cunard and Celebrity ships. We took the Celebrity Century from San Diego to Hawaii a year ago, and they had 3 dance orchestras. Small, but very experiences and accomodating. The Filipino group,called: "Cielo" had an excellent singer, took nearly all requests, and even looked up "Never on Sunday" for me. They also played any latin favorites, and had tables with restaurant and bar service at tables next to the dance floor.