Dennis,
When searching for a Spanish language program, one very easy trap to fall into is the "clearing houses" so prevalent on the net. These websites list dozens of schools; you'll pay more to attend a program you book through an outfit like, Ameri-Span for instance than you would if you attended the school on your own.
IPED in Eredia is an excellent school with a good homestay program. ALISA has a modern facility and excellent courses. The Forrester Institute (Instituto Forrester) is an option. There are literally dozens of Spanish schools all over the valley. Most include some sort of cultural component, cooking, dancing, museum trips and ecotourism as either an included or optional part of their program.
Many CRT'ers have attended CRLA; its location may be the reason, as it's close to everything.
I interviewed at nearly two dozen schools. Almost all of the schools' initial introduction process included an interview with an absolutely hot looking woman, except ALISA and a school outside Alajuela whose name I forget. Interesting marketing tactic. At one of the schools, the flirtatious tica who was giving me a tour leaned into me "accidentally" and slyly suggested that if I wanted to really improve my Spanish, I should have a tica girlfriend.

I presume she was not to be the one; she took my hand while guiding me and I felt the gigantic diamond (presuming here) on her left ring finger!
The family homestay is a good idea for immersion, but keep in mind that you won't be living in a hotel. Late night exits/entries will probably not be tolerated, let alone bringing a puta back to your room with you. You'll eat what the ticos eat, and will certainly have the chance to interact with the locals, but otherwise your social life will be restricted a bit.
Hope you find a good program. Six weeks is a long time to study, but you'll have half your weekdays free anyway and a good excuse to stay in C.R. besides.
BTW, I've read that it is possible to study Spanish at the University. This would be a better option for meeting ticas than the schools, which are aimed at foreigners. That being said, many of the Spanish programs also offer English programs for Spanish speakers and hold "cultural exchanges" so that each can practice the language of the other. This could also be a good place to meet ticas.