"The best hike in the area is at Cerro Chato (I'm actually going there to hike today). This is an extinct volcano next to Arenal that blew it's top thousands of years ago. There is a green lagoon crater lake to reward you at the top. It is a physical hike, so be prepared with water. It costs $10 to enter (unguided) from the Green Lagoon Lodge (near the La Fortuna Waterfalls). If you want a guide, you can get one from one of the local tour operators, though be prepared to pay a premium.
If you are looking for a hike that is less physically demanding, you could go to any of the volcano trails. The Los Tucanes Trail in front of the entrance to the Observatory Lodge is a good one that will take you to the old lava flows."