The way you think about this is wrong. It’s not only about the country you are going to, but also about the home country you leave. If you travel, 4 countries a year for 3 months each you will avoid paying tax. Mainly because the countries you visit will see you as a tourist who stays just 3 months. They will not come after you. And if you travel all the time they also will not have your address.
The main rule is that you have to pay tax in the country where you have your main presence. That is why most countries require you to stay for 6 months + 1 day.
If you leave your home country but keep a house there, you car, your medical insurance, bank account and other things and you come back after some years of travelling there can be a bad surprise for you.
I would concentrate on the requirements of your home country, not on the requirements of the countries you are travelling to.
I live in Thailand. Thailand has a visa for retired people over 50 years old. It is easy to get. In Thailand you do not pay tax on income from abroad if it is brought into the country the year after you made the money (or later). So not in the same year. In for example Bangkok you can rent a condo for about USD 300 a month with a 1 year contract. It allows you to have a permanent address. It is easy to get health insurance, a driving license. And with a 1 year rental contract it is also easy to open a bank account. Bangkok has a great airport with airplanes leaving to almost all destinations, and it can be a good hub to explore the countries around.
I believe that Cyprus also has an interesting program for people moving there and starting a company. The first x years are almost tax free, and you do not have to stay as long as in other countries to be a tax resident. I forgot all details. But I am sure you can find that online.