There are at least 3 places that could be "the marina": Puerto Abrigo in the north, the Caleta next to the Presidente, and the FONATUR marina just north of the Caleta. There are a couple of other candidates, but these are the ones that are "real" marinas by anyone's standards and where dive boats are involved. Caleta is where we nearly always get picked up and dropped off and these days has tons of parking right by the boats. Fonatur has more facilities but the parking can be pretty far away, and seems farther if you're lugging gear.
I get the sense that driving into town and having lunch at one of the hundreds of good places then driving back would involve a time crunch, but there are more options in town than you'll ever be able to try. There's a brief list of some good ones at
Casa Suzana - Lunch
You could explore the various beach bars along the highway. Those are enough closer to Caleta and FONATUR that you'd likely have more time. I know at least some are open for lunch, though I don't know enough about any to recommend them.
You could take lunch with you. Many of the great things available for lunch sell out as to-go orders in the morning long before lunchtime. Lots of Mexicans buy lunch on their way to work in the morning. Think lechón al horno at Tamarindos on Saturday and Wednesday, or cochinita pibil on the remaining days, relleno negro every day. Tortas from all sorts of places - I'm especially partial to shrimp tortas from El Chino Marinero II or El Camarón Dorado. Empanadas, panuchos, salbutes, or chilindrinas from El Resbalón. The chicken places may be open early enough for you to take roast chicken with you - Rosticeria El Pechugón has roasted potatoes that sit under the chickens and basted in chicken fat which are amazing. The Mercado Municipal has places that sell cut fruit and a number of places that sell antojitos that you can get para llevar. In terms of a variety of good food taking lunch with you in the morning might be your best bet, but there won't be anyone bringing you ice-cold drinks (unless the posole Maya guy happens by) and the shade and seating options are limited.
We've bought lunch at the Caleta when a guy on a scooter is selling kibis or whatever, but that's always catch-as-catch-can. I wouldn't want to center lunch plans around that possibility.
My Mexican friends eat a ton of burgers and nachos, btw.