Recently I've colonized a whole lot of Caribbean islands. For this I primarily blame GOG.com.
For those not familiar with GOG, it stands for Good Old Games, and they sell all kinds of older games in packages easy to run on modern devices. They have some newer stuff, too, but I almost always go there for the older stuff. Recently they had a sale on the older Anno games, and I ended up with Anno 1503, 1602, and 1701 for less than $10. After reading a few things around the 'net about the three games, I decided that I only needed to play 1701, as the others are mostly just older versions of the same game.
series of city-building games, with a significant emphasis on trading and economic activity. The series has been in the news recently with the release of Anno 2205, which very well may have been a factor in the GOG sale timing. I'm chronically behind on video game releases (often by years) so playing a 9-year-old game at the same time as the latest release in the series is pretty normal for me. A release from the mid-2000s is right about my sweet spot: old enough to be cheap, new enough to have reasonable graphics and other technical aspects, and I can easily get info about whether the game is worth playing from friends and the Internet at large.
Anno 1701 takes place in a colonization era, as you'd expect from the title, putting you in charge of building colonies for the Queen. You're expected to do the multi-tier approach to building up your colony that is common to these kind of simulation-builder games. Start with small buildings and cheap trade goods, work your way up to bigger/better/more expensive things, and try not to go bankrupt in the process.
The real meat of this sort of game is the open-ended gameplay mode, and Anno 1701 does a good job with it. You can play forever if you like, or set end-game goals. Play by yourself or with AI opponents. Run the risk of natural disasters, or be assured of smooth sailing. Lots of options are provided to make the game as easy/hard as you'd like. My personal style is to mostly avoid military conflict and build up a thriving economy, and Anno 1701 lets me do that without interference if I so choose.