I do suggest you Skymates, in Texas. It's a very friendly school and not expensive at all.
Another flight school that I would suggest is Century Air, in New Jersey but very close to NYC.

Do you actually have personal experience of either of these two schools?
I ask as a few months back you had not commenced flight training so wonder what you are basing this recommendations on?

Captain Mainwaring

You sent me an email but the reply bounces, and you have also disabled any replies via this forum :)

Why is there so much variation in cost for the FAA IR at different schools?

I know there are many factors that can change and different overheads between large schools and the mom & pop type, but in the links above we have one school charging under $4000 for an IR and others around $10000.

I haven't looked at the different companies but there could be several factors.

Old plane vs new plane ... Speaks for itself
Location... Some parts of the country, aircraft rental just costs more
Simulator... Use of a simulator brings down costs a little typically
Part 61 vs Part 141... Part 141 utilizes a lot more dual training, so you are paying for an instructor on every flight.
If it is part 61, maybe they are adding the 50 hours x-country requirement to the course, but like I said I haven't looked at the websites