I have heard "That place is unstable" when talking about places where there is a lot of unrest and it seems like the government will collapse. If you're talking about a dangerous place, for example a city with a lot of crime, you would say: "That place isn't safe" or "That is place is unsafe".

I haven’t heard anyone used “unstable place” in that meaning. You can use that like “unsafe place” which will make more sense.