There are two coffee shops in La Fortuna of note. If you just want coffee, either Rain Forest Café & Restaurant or My Coffee (located in front of the park) will serve you well. However, if you also want a bite to eat, hands down Rain Forest Café is my suggestion. They have a varied menu from the typical coffee shop pastries (and some very delicious cakes), American foods, and typical Costa Rican food as well. It is easy to find as well. From the south east corner of the park (the corner opposite the Super Christian Grocery store) take the road heading south (the one next to the grocery store) and Rain Forest Café will be on the right hand side within about 50 meters.
If you’re looking for something “local” but not really feeling like a whole plate of food, they have some awesome sandwiches for under $2. They’re listed on the menu as “prensadas”. My personal favorite is the pulled pork with cheese sandwich. Ask them to add avocado and you might even call it a healthy option (or I just have very low standards for healthy food). Their nachos are also very tasty as well, and you can get them with the same pulled pork they use in the prensada.
Personally I am not a coffee drinker, but despite my distaste for coffee, the chilled drinks at Rain Forest Café are delicious (even with espresso in them). From the unfortunately translated Placer Propio (listed on the English menu as Self-Pleasure) to the jungle inspired Mono Loco (Crazy Monkey) there isn’t really a drink on their list that I wouldn’t recommend. Also my coffee loving wife and father both tell me they have top notch coffee, unlike the low grade stuff you’ll get in the local bakeries.