Guatemala used to have one of the best reputations for cheap language immersion classes. DW and I spent two months there to kick off a four month trip through Central America in 2010. I spent a month doing Spanish classes in three different schools. DW gave up on the immersion after a couple weeks, and opted to do some mayan painting and cooking classes instead. Antigua, Xela, and Lago Atitlan were the most popular spots and had the largest network of schools.
We spent the first week living with a host family, then opted to move into our own apartment for the next couple of weeks to have a little more privacy. I think the cost for 1-on-1 lessons, 5 hours per day, was $80 to $100. At San Pedro, Lago Atitlan I paid $60 for 25 hours of weekly, one-on-one lessons. This often included either free, or low-cost activities after language classes such as trips to natural hot springs, salsa classes, trips to the market, horseback riding, or volcano climbs. I was glad I never committed to no more than 2 weeks at one school because it gave me the option to look around after I arrived in the country.
A lot of the schools in Xela were based around or supported local charities. After my first two weeks with one school, I opted to move to a school founded by and supporting single mothers. We grew tired of the larger city, so decided to move on to Lago Atitlan for more outdoor activities. One of our friends took classes in Antigua (which are slightly more expensive) and bartended there, and loved her experience. Antigua is a gorgeous colonial city, Xela is a larger, more working-class city in the highlands close to a lot of traditional indigenous villages, and there are a handful of different cities around Lago Atitlan that have access to beautiful natural areas. At the lake, we stayed in San Pedro which is the cheap, hippie/backpacker village but there are other, more upscale options there.
During a subsequent trip to Mexico, I was talking with a girl at a hostel who was studying in a small class in Oaxaca but paying at least twice what I paid for one-on-one lessons. The exchange rate is currently pretty favorable in Mexico so it is probably a bit more competitive.
I love both Mexico and Guatemala. Guatemalans are some of the friendliest people I've met in all my travels, and I felt safe everywhere I went (just make sure to not spend any time in the capital if you go there).
I posted a link from Tim Leffel, who lives in Guanajuato, about different destinations in Mexico yesterday. It looks like @FRx is enjoying studying Spanish in Oaxaca:
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A couple of the considerations I'd make are time of year for travel, and what kind of activities you and the family would like to do in your downtime (i.e. beach vs. mountains). If you are there for a few months, you can pick and choose from a few locations
It gets hot in the summers, so higher elevation or access to a beach would be nice.
You can also probably link up to some interesting opportunities through the local Catholic Churches down there.