September and October are the rainiest months of the year usually. But that doesn't mean that it rains all day, every day. The mornings are usually dry and sunny until mid-day. Then it starts and it's usually only a short rain (a couple of hours), but can rain the rest of the day. Find something to do indoors while it rains.
Women love to do it while they can hear it raining outside. And if you're adventurous enough, ignore the rain. It's not a tropical monsoon after all, sometimes it's pretty light.You have to be an early riser in the rainy months. If you get up by 7am (sun's out by 4:30, dark by 5:30), you have 4-5 hours to hit the beach and some of the adventure tours (Do a zip line tour, aka canopy tour). If you like to sleep till noon, you should go during December-March months where it hardly rains.
The nicest resorts and beaches are on the West coast in the province of Guanacaste. Try town of Flamingo, Tamarindo, Samara, Nosara, Playa Coco. The Carib coast is nice too but I didn't see too many nice hotels/resorts there. It's mostly rustic hotels (many don't have A/C). Limon is a dump, you're right.