Actually we get our to go drinks from all the bars seasonally open. Both pools , narcoossees, citricos and mizners all will do it. I say this because 1 may be closer to you or 2nd one may have a drink you like the others don't.
Last year dd tried both pools, mizners and citricos for a strawberry daiquiri . When she came back to me sitting in the lounge at sl without one the manager asked her why? (we had been chatting)When she said she couldn't find one he called narcoossees because he thought they had and confirmed before she went to get it. Then when she got back he also comped the room for her efforts.
Another reason we say gf has the best service.
You can also get lapu lapus from poly in the pineapple to go and carry back. The walk isn't too far between the resorts.