Hi Elizabeth,
I would recommend you make at least a reservation for your first night in each of your destinations, Arenal, Central Valley, the Southern Zone. That way you have a place to go when you first get into the area but then you’re flexible to change locations during your stay.
In Arenal you’ll find plenty of hotels near the town of La Fortuna and also around the lake, and there are several places along the coastal highway in the Southern Zone, especially around the towns of Dominical, Uvita, and Ojochal. But the Central Valley isn’t really a tourist area at all, so there are a lot hotels in and around San Jose, the capital, or near the airport. Those are easy to find. But the ones in the rest of the Valley are more spread out and harder to find. That’s where you might want to do some extra planning.
May is the start of the low season, so you shouldn’t have much trouble with places being fully booked in any location.