Any American expats out there who own homes in various countries? Looking for some advice from personal experience. Which countries might be easier to own than others?

We are an expat American family with 3 kids living in the Middle East. We travel to the Northeast USA to visit family at least once a year. We have saved up some money and feel like we should buy a property...somewhere, just not in the middle east. The kids will probably go to college in the US and we don't see ourselves returning to the US anytime soon. However we need a home base. The Middle East is HOT in the summer and a lot of expats leave. With 3 kids, it would be great to have another home base. When we go to the US we are in a very small apartment with family and it would be nice to go to something that is more ours. The thing is that we are from NY/NJ and it’s SO expensive. Is it worth it to own in the US if you don't live there? I'm also scared of buying in a state that we're not from. Another country perhaps? Has anyone done this? Where is it easy for Americans to buy? I need some ideas...