The warmest months in Punta del Este are January, February. Punta del Este or the beaches of Rocha are good. One thing to note, you will want a car for PDP. Otherwise you will be rather constrained to one area or another or taking cheap buses -- not convenient except to connect various "centers" within Uruguay -- or rather expensive cabs -- at least in/around PDP -- to get around. There is also José Ignacio which is a bit more secluded and then some. Atlantida or Piriapolis are more busy with family vacationers and day-trippers.
I am not a big fan of the Conrad in Punta del Este although the breakfast/brunch is complete and one of the better ones across the Hilton brand. The breakfast is included for free for Gold and Diamond members. Unfortunately, one must not expect much of an upgrade -- if any -- as an HHonors Gold or Diamond member since the hotel does not much seem to care about Hilton status. You might find a rental house or service apartment a better deal and/or more individual.
If the weather in PDP is not cooperative, Floranopolis is in Southern Brazil and can be a wee bit warmer than PDP at that time. Or go up toward Rio -- and further north -- in Brazil where the warm weather is more likely to be consistent. (If interested in Brazil, make sure to get the visa and note that for Americans if you don't use it within 90 days, the visa goes stale and becomes absolutely worthless.)
Getting by with English and/or French in Brazil is far harder than doing the same in Argentina or Uruguay. Just something to keep in mind.