Below you have a chart to help you decide when you might wish to visit.
Back in 1955 -59 a Dr. Archie Carr from University of Florida wanted to protect the area. Due to his work Costa Rica now has the Tortuguero National Park. This area is well protected today. To see the turtles hatching at night you must have a trained guide. Cost about $10 – $20 depending on a number of factors. This is just to take you out to the beach at night.
You can drive to Tortuguero, (well when I say drive, it is wishful thinking) the below map gives you an idea. From my home to Tortuguero it is about 4 hours. (A to B) From San Jose the capital about 4 to 5 hours. There are toll roads as you leave the capital, San Jose.
If you drive to the area of Tortuguero, when you arrive you will still need to take a boat taxi over to the actual town of Tortuguero to visit the national park. You may not want to leave your vehicle alone. Not a good thing. Plus to drive to Tortuguero you need a Jeep with a winch, snorkel and very larger tires. If the rivers are flooded you will not make it to Tortuguero.
Most tourist take the boat from Limon to Tortuguero. It is faster and in most cases safer. You can take a lot of wild life pictures as you travel up stream on the boat.