Traveled there a couple years ago. Geography mostly boils down to Caribbean side, Pacific Side, and Cordillera. Caribbean side has some surfing, but pretty quiet and not much development or infrastructure. I doubt there's a surfaced runway. Sketchier drinking water and malaria more prevalent too.
Pacific side has the bigger cities and ports. Nicoya peninsula to the nowrthwest, which gets a bit more of the gringoes-on-spring-break scene. Good place to start if you don't speak any Spanish. Down coast on the Pacific side is the Osa peninsula. Quite rugged and remote, and very beautiful. Access is by boat and dirt road, mostly.
The Cordillera has great sightseeing attractions like volcanoes and rainforest preserves. Arenal Volcano is famous for being in the cloud most of the time, and the rainforest could probably also be categorized as cloud forest, so in terms of the flying, probably a fair bit of scud to be expected in the Cordillera.
A word of caution- Driving in the capital of San Jose will make flying your Sportsman into LAX look like a cakewalk. We had four in the car, and it required everyone constantly on high alert calling out traffic, in order not to get lost and/or killed. Apparently it has the highest rate of pedestrians deaths of any latin american city. Then, there is the Pan American highway. I used to dream about riding a motorcycle along the length of it until I actually saw it. The section south out of San Jose is known as Cerro De La Muerte, which translates to "Mountain of Death." That seemed quaint until we came upon the first charred wreck, still smoldering. It wasn't the last.
Apart from that, the country is great. Especially if you can learn a little spanish, enjoy birds, sea turtles, monkeys, sloths and other tropical wildlife, and friendly locals once you learn the ropes and lose the tourist mentality. You can get a fantastic breakfast of beans, eggs, farm cheese and Lizano sauce which, taken in context, is just as great as the reindeer fry-up at Gwennie's.
Good luck, and sorry to hear about your troubles. Costa Rica sounds like as good a place as any to ride them out.
-DP