Costa Rica is Latin America Lite. Ticos (Costa Ricans) speak a clear Spanish with some unusual regional slang, but the country is very heavily touristed.

I'd suggest finding a spot without much of a tourist/DN scene. Argentina/Uruguay and Chile all have very particular accents in Spanish. The Caribbean basin (e.g., Puerto Rico, Cuba, Dominican Republic, Caribbean coast of Colombia and Venezuela) also has a difficult set of accents, with a lot of dropped consonants and sometimes entire syllables, also very rapid speech. Mexico has the greatest media penetration in the Spanish-speaking world, and everyone understands Mexican Spanish, although it can sound rough to non-Mexican ears.

I'm just going to throw out a few suggestions, and a bit about why I include them (far from exhaustive, based only on my own experiences as a fluent but foreign speaker of Spanish):

-Esteli, Nicaragua. It was a center for Eastern Bloc volunteers to learn Spanish after the Sandinista Revolution at the end of the 70s, and there are still language schools operating there. It is very, very off the beaten path for tourists, but quite a pleasant little town.

-Manizales, Colombia. It's safer than Medellin and Bogota, pleasant highland climate, crystal-clear Spanish accent, and a gorgeous setting. There's foreign tourism in Manizales (and also nearby Eje Cafetero cities like Armenia and Pereira), but not enough to prevent Spanish immersion.

-Xalapa, Mexico. Lush green regional capital (Veracruz state), large student population, off the tourist beaten path.

-Xela (aka Quetzaltenango), Guatemala. Super cheap working Guatemalan city, you would definitely be immersed in Spanish there. Flores, in the northern part of the country, is also a great place to spend some time immersed. It's a small town on an island in a freshwater lake, about an hour from the magnificent ruins at Tikal. Antigua is super popular with people purporting to study Spanish, but you'd experience a similar level of Spanish immersion at a Guatemala Pavillion at Epcot Center, if they had one.

-Lima, Peru. Great food scene, big city, low cost of living, enough locals to dilute the significant English-speaking tourist presence. The predominant Spanish accent is easy to understand throughout the Spanish-speaking world. Major international airport makes getting in and out easy.