Volcan Arenal is great if you want to try something other than the beach. There are some expensive, but really nice hotels with their own thermal hot springs. Our favorite hotel is the Observatory Lodge. It isn't as fancy and doesn't have hot springs but it is the closest to the volcano and the hiking up there is fantastic.
Monteverde has the best ziplining in the country and the cloud forest is beautiful, especially if you like birding, but in my opinion, the place is getting too touristy. We met a guy there who tried really hard to get me to go into business with him on a microbrewery. Every time I get fed up with my job, I think about giving him a call.
It's definitely not authentic Costa Rican, but Ponderosa Adventure Park is great for kids. We took our kids there for Christmas last year and they drive you around in trucks so that you can feed exotic animals. The giraffes were a riot. They were pretty aggressive going after our carrots and with their long necks they would come at us from every angle.
One of my favorite out of the way national parks is Rincon de la Vieja. One part of the park is rarely visited but it has some natural hot springs that you can swim in. The other part of the park is full of bubbling cauldrons of mud from the volcano. It also has some nice rain forest and a waterfall.
The Osa Peninsula is a pain to get to but it has the best wildlife viewing I have ever seen. You will see all kinds of monkeys, birds, snakes, sloths, and anteaters all in one place. My last visit there, I got to see a tapir, which was on my bucket list.
If you want an Osa like experience without the hassle, Manuel Antonio has some good wildlife viewing. The only bummer for me is how much the area around the park has been built up over the years. I taught a course there and we rented this awesome house right on the edge of the park. Every day we could sit on our back porch and watch monkeys, sloths, and all sorts of birds stop by. We even had some macaws fly by.