We've been to Costa Rica a few times. Its an absolutely beautiful place.
Do's : I recommend Manuel Antonio National Park. I avoided it my first 2 trips, because its "too touristy"... but it truly was memorable and worth it. If you want to go on a zip line tour, many operators have world class options there. Eat at Pablo Picasso's in Playa Negra. You'll see signs all around the area advertising burgers as big as your head. They're good, and not lying! I recommend the fish tacos though. Playa Avellanas is a nice beach with some places to stay. Further south on the Nicoya Penninsula is Nosara, and Sumara... they're funky spots with lots of yoga studios and hippy gringos. Mal Pais is at the furthest point south on the peninsula, I recommend it!
If you want to go surfing, Pavones on the Panama border can't be missed. Its raw an undeveloped, with sloths and monkeys in the trees, and herds of wild horses running on the beach. Its fabulous! Its also a hell of a long ways away from Liberia, so keep that in mind!
As mentioned above, Volcan Arenal is really touristy. It makes for a really interesting day trip, as the vegetation and weather change as you climb in elevation. I liked it, but as soon as I saw it and experienced it, I was ready to go!
Don'ts: Avoid Tamarindo if possible. It's seedy, and lots of drugs and prostitution. We had fun there as 20 year olds! I wouldn't go there now.
Avoid San Jose. It's like any big city in a developing country. Lots of traffic and diesel exhaust. Lots of folks struggling to make a living.