There are oodles of dive charters in West Palm to choose from; just ask the concierge at your hotel and they'll likely be able to get you set up.
However, here's some overall info, starting at the north end of Palm Beach county and working your way south:
Jupiter--a little deeper, but usually bigger critters. I think the consensus would go with Jupiter Dive Center in this area. They operate two boats, and usually, one going out is more "advanced", often catering to the spearing crowd, while the other is a little less advanced. Either way, it's hard to find a reef up there less that 70 feet or so, so Nitrox would be very wise if you want more than a 20 minute limit (their rule). http://www.jupiterdivecenter.com/
Riviera Beach/West Palm Beach-- Most of the West Palm Charters are docked at the Riviera Beach Marina, with a few exceptions.
Out of Riviera Beach Marina:
Narcosis, if my memory serves is the largest of the general offerings...more open deck space, more crowded if you hit them on the wrong day. http://www.narcosisdivecharters.com/
Pura Vida--A little smaller boat. Great crew. If you need to rent any gear at all, the drawback is that their actual shop is a mile or two away on the other side of the Blue Heron Bride--a bit of a time stealer if you're running late for the boat. http://www.puravidadivers.com/index.html
Oceanquest/Sandy's Sunday (not sure where they're docked): you've had a few recommendations for. I'll leave the detail to others as I haven't gone out with them before. Website: http://oceanquestscuba.com/
Just north of Riviera Marina--
Jim Abernathy Scuba--Another larger operation. I believe they generally operate two boats, usually one for more advanced and one for less advanced divers (generally split up by depth requests). It's been years since I went with them, so I can't recommend one way or the other.
http://www.scuba-adventures.com/
Going south, the next cluster of dive ops is in Lantana/Boynton.
Underwater Explorers out of the Boynton Beach Marina is indeed the big favorite of many of us on the board. Owner/DM Kevin is part of the experience. He's adamant about keeping the boat as a 6-pack, so it's often a boat full of just people you know. Handy. Underwater Explorers - SCUBA Diving Boynton Beach, Delray, Palm Beach, Reefs and Wrecks
Starfish Enterprises is just north in Lantana--someone else mentioned them here as well.
http://www.idivestarfish.com/
DCI Charters runs the Little Deeper fleet--one of which is still run out of Boynton, just next to Kevin's boat. The captain is a curmudgeonly old guy, funny as can be, and my recollections of diving from his boat are that he seems to carry more spearfishers, though I haven't been out with them in some time......
http://www.deeper-dci.com/
As for beach diving, the only well known dive is under the Blue Heron Bridge--great for macro stuff and sighting juveniles of all sorts.
Beach Diving--There is only one well known "beach" dive in the Palm Beach area, under the Blue Heron Bridge. It is subject to tide fluctuations. http://www.wadespage.com/D800DS06RF01.shtml
Enjoy Palm Beach--not a bad place to visit! Be prepared for afternoon storms from around 3 to 6 pm.
