I travelled around the world for 6 years and the number one impediment to staying in any country was the visa situation. If you are staying there longer than a tourist visa, and especially if you want any kind of employment (or are in a situation where you are visibly employed) the red tape in the vast majority of countries is very tough.

The only exceptions I know about are Chile (which gives one year visas that are relatively easy to renew) and Panama (which will give you residency if you start a business there, it can be a small one.)