For what it's worth, I studied masters in another country and moved to EU due to visa issues , but I didn't like the experience. I had the BlueCard and was eligible to receive the PR but didn't pursue it. People are quite racist and sometimes I even got yelled at when I was minding my own business.
That being said, yes, you can travel to all EU countries, and food and chocolates in EU are far better than even US due to government regulations.
WLB in Europe is not much different unless you join a low TC local company like Bosch or Siemens, which pay extremely low wages. Housing is expensive, and even a small studio costs 1500 euros. If you happen to need specialist appointment or scans, you would need to wait a longtime. Grass is always greener