I would recommend talking to Henley & Partners, they help with resident-by-investment, aka golden visa. It would help you focus cost, plus add a passport to your portfolio. Spain I think it’s currently €500k, while Greece is €250k, and and St Kitts and Nevis is €200.. I think Mexico was around $150k last I looked at buying.
As mentioned, you won’t have the same buying power with banks as you do in the US. In the EU they basically run credit via bank deposits, their credit cards are more like debt cards. HSBC can help you get checking accounts setup in almost any country.
We are taxed on our world wide income in the US, but that’s not that big of deal, as we have treaties with other counties to help avoid double tax, and you can always setup up IBC in Cook Island, or St Kitts & Nevis, thus off shoring the income earned outside of the US, if you bring it home you will have to pay taxes on it. You will need a good CPA for all this, because the IRS loves people who have tax haven access.
Vacation homes are nice, but you won't find the same ROI you get here in the US, and houses can sit for a long time before selling. Personally I would stick with US vacation destinations before I would go after AirBnB in another country.