I'm not saying you should not stay overnight in San Jose that day/night. I AM saying that you don't NEED to do it that way.
I've only dine it once, but I recall the ride from SJO to our hotel in La Fortuna took about 2.5 hours. Surely you'd be able to enjoy yourself if you get to the Arenal area in the middle of the afternoon. This is why I say you don't NEED to stay overnight in San Jose if your flight lands at 11:30 in the morning.
Our flight landed around 1:30 p.m. or so. After getting our luggage, clearing customs, and then waiting way too long for our pre-arranged and pre-paid private transfer, we arrived at our hotel around 5 p.m. or so, if memory serves.
I will strongly recommend AGAINST booking a ride with JJ Tours, as my travel agent booked for me. They were supposed to be there waiting for us and were not. I had a local phone number for their office buy there was no answer. When someone did finally show up with my name and hotel name on a sign, he walked us across the street towards the parking garage and then down the street away from it. He then calls someone on his cellphone and about 10 minutes layer a driver shows up and the man tells him where to go. As we get into the vehicle, the original man gets in my face and sharply demands a tip from me. I shrugged or something, and he angrily said, "I find you a ride and you no tip me?" I was intimidated by him, and rightly or wrongly I gave him a tip because, frankly, I was scared of him and the way he was acting. We weren't around crowd if people, we were up th road from the terminal, it was my first hour in a country I was unfamiliar with, and I didn't know what would happen next.
Needless to say, I will never recommend JJ Tours. The driver he subcontracted, however, was friendly and helpful and I wish I had noted HIS name and contact information so I could publically recommend him as a driver.