melissa: Sounds like a great gift for you. Nice Dad!
$500 is fine for one week's expenses if your hotel, airfare and car are paid for.
Food: Most hotels will provide breakfast so that leaves you with the rest of the day. In Costa Rica, a restaurant that serves typical Costa Rican food and is inexpensive is known as a "soda." You can get good food at an excellent price - and lots of it! One dish that is popular is known as a "casado" which traditionally has six items: some kind of meat, fish or chicken; rice, beans, salad, and two "cook's choice" which could be a different kind of salad, a slice of cheese, half an avocado, a sauteed plantain. It's a LOT of food and for many people, it's two meals.. Typically, a casado will cost around $7. Otherwise, you can shop at local supermarkets for fresh fruit, cheese and bread from a bakery and just make your own "picnic." There are "fast food" chicken outlets most everywhere and some of them will feature fried chicken as well as "pollo asado" which is chicken roasted over an open fire.
Activities: Yes, most National Park charge $10 to enter. If you still have your college ID, you might be able to get a student discount. Bring it and show it to the ranger and see what happens! Since you have your own car, you can drive yourself to National Parks or other excursions and save the money you would have spent on an organized tour of some sort.
For horseback -- ask at your hotel and around town to find the best deal. Make sure the horses are in good shape before you pay and go.
With one week, you will have to make some choices. Two locations is really the most you should try for. Under the circumstances, I think you will be better off choosing Arenal and someplace in the southern Caribbean such as Puerto Viejo or Cahuita. I think you will find the Caribbean less expensive and less touristy than Quepos/Manuel Antonio.
Some helpful websites: www.arenal.net or www.fortunawelcome.com
www.yourtravelmap.com - for distances and travel times
A good website to look for some activities in the southern Caribbean: www.ateccr.org
The airport is actually in Alajuela, not San Jose. There is lodging (and food) of all sorts and all prices not far from the airport without the hassle of going into San Jose.
Edited: 8:50 am, July 10, 2013