There's really two parts to the question . . . for most folk the idea is wrapped around something authentic that represents the country they are visiting and the second part in the minds of many (optimistically) is the idea that perhaps you can support the local economy in some way.
There are very few uniquely Costa Rican items anywhere in the country because in large part, unlike a number of other latin countries, Costa Rica always had a very small indigenous population (the reasons for that means you're just going to have to visit to find out).
As you plan a trip to Costa Rica, you may want to think about adding these places to your itinerary to help support local folk. You wont find a "hecho in Mexico" or "made in China" in any of these places.
In You can also visit Boruca - about 5 hours south of Alajuela (relatively easy to get to, drive past Manuel Anatonio) and a spectacular visit in a beautiful village where most of the folk are somehow connected to the selling of intricately carved and painted masks and the police station is shuttered closed. You need a 4*4 to get to the village but worth the effort. Local residents Mike and Lara are helping with a web site here: http://www.borucacr.org/help.html
You can visit the Maleku if you travel to Arenal as do 80% of our visitors but nearly nobody goes another few km to the Maleku reserve. The Maleku can organize tours for you that your hotel can hook you up with to visit things like poison dart frogs, medicinal plants and a "museum" (really a twig hut but a great visit where you may be able to find a necklace made from Gar fish scales). The people are wonderful and need your support . . . they make some art such as rain sticks, iguana covered drums etc. Not far from the Maleku reserve 9and a great local place to stay) you'll find our friends Steve and Debbie at : http://leavesandlizards.com/You may not have heard about the Chorotega? Yup right on your way to the northern and central Guanacaste beaches near
You can visit the Bribri in the Caribbean zone . . . take a day trip to Yorkin (if your trip includes Puerto Viejo or Cahuita), a delightful indigenous group - and the largest in Costa Rica . . . the trip is by dugout and they make chocolate, bows and arrows as well as the occasional painting (which you should snap up because their output in nearly zero). If you're in the neighborhood you might try staying at Wendy's here: http://www.cashewhilllodge.co.cr/ - a great base for exploring the area and visiting the Bribri
Many tourists also visit Sarchi, the home of the woodworkers of
Finally, there are more but you'll also find interesting things in some hotel gift shops - look for locally produced items - often wood, some home made textiles but sometimes some nice ceramics - in particular the famous PEFI ceramics (which you can find at the Pura Vida and a few other nice places) made by the daughter in law of Don Pepe Figueres (the guy who established modern Costa Rica and no doubt pondered peace in our time after he abolished the army in 1948 while sitting in a famous Sarchi rocking chair).