I haven't seen luggage storage at the airport for a while, and it seems to me that the storage options of old have been done away with in the time of terrorism. Any unattended bag is hauled away and dealt with so I doubt that they'd allow you to leave it somewhere in such a case. You could try to check in and then only be responsible for your hand luggage, but I think they have a rule on that too--only 3-4 hours in advance is allowed. If you are looking for a jaunt to the beach for the day, you may be able to book a cab for the 4 - 5 hours that you'd have free (they'd want you back at the airport 2 hours in advance and processing the line to pass security can take 10 minutes or 45 minutes depending on time of day and day of the week) and leave the luggage in the vehicle.
If you have a "layover", is it possible that they would have checked your luggage straight through and, again, you'd only have a purse/camera bag/carry on to be responsible for?
When totaling costs for a cab to a beach/hotel and the price of a day pass if you choose to go that route (not usually less than $50), you'd probably have to factor in the $10 per person entry card fee in order to be allowed to leave the customs area of the airport. They may not want to believe you if you say you're returning to the airport in mere hours, even if you do produce your ticket as proof, and choose to enforce the rule. I know that this has happened in the Santo Domingo airport in a similar instance. If you come from the tarmac and intend to leave the airport, they will assume you are arriving in the country.
7 hours in the airport would certainly be a trial, but there is a funky eatery in the lounge area of the higher gate numbers (5 and up), you can buy beer easily, the music store in the lounge of gates 1 - 4 is blasting merengue/bachata/salsa music all of its open hours, and you can pick your choice of areas to relax and play cards or do what you'd like to entertain yourselves. Waiting in line for a washroom can often take 20 minutes if you're a woman, so be warned about that.
Kaki