Civilization 5 is awesome. Very engaging, strategic, with some historical basis, and some battle tactics. You will be up to 5 am wanting to play just one more turn. If you have never played a Civ game, you might try out Civ 4 or Alpha Centauri for cheap. Alpha Centauri is the most polished, but Civ 5 is the more interesting game.

Since you are a sailor, I also recommend Sid Meier's Pirates! It's not very new, but you sail around in the Caribbean firing cannons at the French, British etc. and taking their loot. It's a simple game (there is tacking and wind shifts though), but it's very fun. There are even some turn based battle mini games that you play while raiding a port.

For a unique and shorter game, I like Braid. It is something like $5 on Steam and you can go through the game in a day. It has some unique puzzles and is supposed to be set in a painting.