Check the EASA list of approved overseas ATOs:
https://www.easa.europa.eu/download/...rtificates.pdf
Also keep an eye on the ones who are no longer EASA approved:
https://www.easa.europa.eu/download/...rtificates.pdf
Keep in mind you can't do the full instrument rating outside Europe. You'll need to do the flying part of in within European airspace. The schools can help you with this. You can go as far as CPL and multi engine in the states, but some of the IR will have to be done back home.
I did some hour building in Pilots Paradise in Sebastian, FL who are a good crowd to deal with. Their EASA instructors are from the UK and Spain.
They also have a connection with European Flight Training in Fort Pierce who have a good reputation too. I'm not sure what the employment prospects are like for their trainees, I know in the past some airlines turned their noses up a little towards US trained pilot and preferred those who stay in Europe. Not sure if that's as much the case now.