First of all, there is no obstacle to getting a second citizenship on the American side.The Supreme Court has ruled several times that Americans cannot be forbidden from acquiring other citizenships. So keep that in mind because if you really like a country, it's always best to become a citizen if you want to stay there.
There are many countries where you can live and retire indefinitely. For retirees, countries have visas that allow you to remain indefinitely as long as you have sufficient income from pensions and investments. In Europe, they include Portugal, Spain, France, Italy, Greece, Cyprus, Germany, and several countries in the Balkans. Popular retirement visas in the Western Hemisphere include Mexico, Costa Rica, Panama, Colombia, Uruguay, Brazil, Argentina, and Ecuador.
The key factor for all of these visas is whether you have enough passive income from pension and investments to qualify. The cheapest are in Central America, with Costa Rica and Panama at $1000 a month. Europe is more expensive although Portugal will grant AD7 retirement visa for around $1000 a month income. All the other countries are in the €3000 to €3500 monthly income range.
Finally, note that although you often need to renew the visa annually for every two years, this is just a formality to show that you continue to have enough income. Many IL subscribers have lived for years abroad in these countries in this way.