Where are you staying. Coolers are fine on the beaches. Availability of beach bars/restaurants depends on what part of town you are staying in. In the hotel zone most of the resorts are guests only but in the Los Muertos area (southside) there are quite a few beach bars. Knowing where you are staying will help you get a clearer answer.
Drinks on the beach
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Walk to the marina and buy some drinks and take them back.. There is also a store down the street as well. Then go through your hotel right down to the beach and drink them there.
if you venture to old town (los muertos beach) many of the beach restaurants have 2x1 happy hour, also andales has 2x1 in the afternoons.