I am looking at this question from the perspective of flight times from the U.S. as the initial criteria then the other criteria such as convenience, total cost, variety, and camaraderie.
Direct non-stop flights from Southern California (LAX) take around 6 hrs to get to San Jose. I looked on some web sites to see what it takes from other parts of the country too. The Florida guys have it best of course with flight times of around 3 hrs. The northeast has it pretty good too with direct, non-stop flights of a little more than 5 hrs from New York.
Given this, it seems that the typical CR monger is not going to want to sit on a plane for a significantly longer period of time. That rules out Asia (Thailand, Philippines, etc) and most of South America (Argentina, Brasil, etc) and probably Europe (Germany, Eastern Europe, etc) as direct competitors to Costa Rica. The real competition for these monger dollars is most likely to come from countries near to Costa Rica or closer to the U.S.
At the northern end of South America the possibilities are Colombia, Venezuela and Peru. They can require a little more flying time but seem to be competitive on cost (or better) with San Jose. Venezuela has political issues that make it less likely to become popular while Peru is just not that well known yet. Colombia seems to me to be the best bet in this part of the world and is the place I'd most like to check out, well aside from Brasil

The downside to Colombia is the perception of crime there, whether deserved or not. In addition it doesn't seem likely from what I've read that we're going to see too many places like the SL, KL or HDR there given the pressure already on the Medellin Mansion.
In Central America, Panama already has a thriving scene, but the prices are higher than in CR and I don't know what the possibilities for CR-style camaraderie are there. I took a look at the ISG for reports on the rest of Central America, and it's not too promising. The Nicaragua section has the most reports, but they're mostly from one guy (Meatloaf). He's very entertaining to read but doesn't make it sound like a great monger spot. The other countries have MPs but don't seem to have much else aside from expensive strip clubs.
Next is the Caribbean. Sosua gets raves here, and I'd like to check it out someday. Cuba has correctly been described by others here, and it's not really going to become a monger destination like CR unless the political climate changes radically. Radical change seems unlikely for the next 10 years though things could slowly evolve for the better. I don't know anything about the smaller islands in the Caribbean, but at this point I'd say that the DR is the best bet there.
Finally there is Mexico. Places like Cancun already have thriving tourist scenes with lots of Gringos. There's no reason a place like Cancun couldn't evolve into a CR. Of course the recent drug violence there could scare away gringo tourists in the short term. However they could be replaced by mongers if CR declines.
I won't consider the U.S. or Canada because it just doesn't seem likely that we'll see bars like the HDR or SL sprouting up anytime soon.
In the end, my guess is that the Dominican Republic would benefit first from problems in CR followed by Medellin. However I think the best bet for a long term monger spot is in Mexico in one of the currently popular tourist spots that ultimately gets colonized my mongers.