I've stayed at Casa del Mar, the hotel just south of Palmar, many times. The closest restaurant is Paprika which also serves Tikila the bar right across the street. About a block south of Paprika is Ernesto's Fajita Factory. Going north the closest restaurant is probably La Hach? Feels like about 4 blocks north of Palmar.
The closest docks from Palmar are probably south of the CDM pier. I have no idea if it's possible, but maybe you could arrange to pay Scuba Shack, or the dive shop that services the Park Royal. I think people staying there pay $5/week to use the dock closest to the hotel. Too bad that CDM won't allow people to pay. They appear to have plenty of lockers now. Maybe the issue comes up so rarely that it'd be a pain to make provision.
If you're lugging gear, I think I'd try to find a way to pay for both dock usage and locker rental. If you dive with Scuba Shack or any of the concierge dive ops at the end of the CDM pier, you're set. The concierge handles, (I think) Pro Dive, Cozumel Marine World, and one other shop, not Dive Paradise. Del Mar Aquatics also has an actual shop on the CDM pier but is no longer affiliated with CDM.
I don't know if you get a locker when diving with the concierge shops, but I'd suspect you do because they're hooked up with CDM, who apparently owns the building where the lockers are located. (And the pier as far as I've been told, though maybe Del Mar Aquatics also has some ownership?)
Same applies to diving with an op that handles your gear. You'd only need to find a way to get on the boat. If you have to take a taxi to the caletta to get on a boat, I think it's 70 pesos from Casa Del Mar to the caletta.
-Blair