Hello!
I went to Costa Rica in late August last year!
I do recommend renting a car, simply because public transportation is very slow, so if you want to move around a bit, having a car will be easier. I cannot recommend enough Wild Rider (
http://www.wild-rider.com/car-rental-rates/) for car rentals. It's a local company, owned and operated out of San José (but I think they might have something out of Liberia airport, you'd have to check). One thing to watch out for in car rentals in Costa Rica is that almost every company is going to quote you the day rate, and then once you get there, they'll tack on the mandatory insurance (Costa Rica doesn't allow car rentals without the country's insurance - your own insurance or even credit card insurance won't be acceptable). Wild Rider was the cheapest by far, simply because their quoted price was EXACTLY what I paid. They brought the car to the airport, and the guy spent an hour and a half with us, not only showing us the car, but mapping out our entire vacation for us. With our paper map on the hood of the car, he asked us where we were staying, and what kinds of things interested us, and then he drew possible itineraries, circled areas to visit, names of the best tours (always local - not touristy places), told us where the locals go for hot springs (no $$ to pay!), everything. It was fantastic.
I recommend the Arenal region, as it was lovely. That's where we went to the local free hot springs. You park across the street from the Tabacon Resort (at the entrance of the Volcano Arenal Park). You walk under the yellow metal gate, walk down the little hill, underneath an old stone bridge, and BAM, free hot springs just across the street from an expensive resort.
Volcano Arenal is also beautiful - we hiked up Cerro Chato, which is in the same park. From its rim you can see the Arenal Volcano. Instead of paying for a guided tour through the park gates, again, stop right before. There's a little wooden hut, and for I think 12$ for the two of us, they gave us a map and indications for the hike.
We also went to Las Pumas Rescue Center (about 5 km from Canas), which is a lovely little park where they rescue injured or animals that were formerly kept as pets. The town of Canas was also beautiful, with a church in the middle covered in mosaic tiles.
Close to Tilaran is Vientos Frescos, which is another private small park with a total of 5 (or maybe 7? I can't remember) waterfalls. It's a lovely short walk and we were the only people in the entire park the whole day. Be careful of the monkeys at the entrance though, they pelted us with fruit when we didn't move along quickly enough.
Also, the Catarata Llano de Cortes, which is a few km outside of Bagaces. Absolutely breathtaking little waterfall, with a pool at the bottom for swimming, you can explore the cave behind it. The entrance is free (it's private property), and you can simply donate to the women seated on the road. They collect money for the local church/school (they'll give you an official receipt). I gave 2$ and some fruit that we had. It's well worth the stop.
After the Arenal region we stayed in Nosara, south of Playa del Coco in Guanacaste. I don't know much about where you're going to be, but Nosara, Playa Guiones, Playa Juanillo... they were all lovely.
There - now you know my entire vacation!
Feel free to PM me if you want more details. Have fun!