You might also consider living in the suburbs of one of the bigger Upstate cities: Albany, Buffalo, Rochester, Syracuse, and Utica. This would give you the advantage of living in a nice, quiet neighborhood as well as being close to amenities in areas with lots of young people.
Sheena's suggestion to look into attending one of the SUNY colleges that offer vet tech programs is a good one. Here is a list of the NYS colleges, public and private, that offer vet tech programs:
Vet Tech in NYS
While as an out-of-state student you would pay more than state residents at the SUNY colleges, it wouldn't be any more than if you were going to a private school, and probably be less than if you were to attend a private for-profit school like Penn Foster. You would also be eligible for federal financial aid, including Pell grants as well as college work study and subsidized student loans that you might not be eligible for at many for-profit schools.