A nice little two-player game that one of my friends introduced to me was Babel.
In Babel, the players are competing to try to build the largest temples. On any given turn, a player will draw three army cards, perform any number of actions (such as building temples, playing armies, using army powers, or once per turn doing a "migration" which consists of moving a group of 3 armies), and then draw two new temple cards that are available for either player to build (placing the lowest numbered one on top of the stack). In order to build a temple, they must have a corresponding number of armies cards present at that location - for example, in order to build a level four temple, they must have four army cards present. However, each of the army cards represents a different race of people. If three of a given race are in consecutive order, then the player may discard one of the three cards to perform that race's special power. Play continues in this way until one of the "game end" conditions is met; basically the game ends when one player has 15 points of temples and the other player has less than 10, or when one player gets 20 points of temples (or if the temple draw stack runs out, whoever has the most points wins). Did I make that crystal clear? Well, there's a reason it's called a "summary" and not an instruction manual. Oh, you didn't see where I called it a "summary", because I didn't use headers? Well, that's just whining...
For the first pro in Babel, I really liked the different races and their powers. Granted, I have not played this game enough to determine if one power seems "better" than any of the others, but in the games that we have played, each race's power had times in which it was crucially important. The Persians (which let you skip a level when building your temple) I initially thought were the weakest of the powers, but I used them to secure victory in one of the games! Some of the other powers are much more directly offensive (one of them lets you rob the top level of your opponent's temple, another lets you "emigrate" (kill) their troops), but finding the correct time to use your powers, while preventing your opponent from capitalizing on his (and maintaining enough units to actually build temples!) is the crux of the game.
The next major pro for Babel is simply what the game itself is - it is a fairly quick, somewhat deep, easy to learn two-player strategy game. There are some of these available (I think this was actually part of a product line several years ago of two player games). However, none of the other ones that I played from that group seemed to actually gel as well as Babel does. It claims to be 45-60 minutes, but I would think that around 30 minutes would be a bit more realistic. To actually learn the game from the rules takes about 15-30 minutes, and to teach it takes about 5 minutes. And yet, while playing the game, you feel like you're actually engaged in a strategic experience where one person legitimately wins primarily based on skill (and there's enough depth to it that the game won't be "mastered" after a couple of plays through). And, to go with all of that, the box is also compact enough that it could pretty easily be slipped into a backpack to be played at a coffee shop or, better yet, at an airport! (Yes, I'm back to really liking games that can be played at airports.) Setup time is incredibly short, and so it is an ideal game for these kinds of situations.
When it comes to cons for Babel, nothing truly jumps out to me like in many other games. That by no means is the same as saying the game is flawless. It simply means that its cons seem more nuanced. For example, I have questions about the replayability of the game. Whereas I have enjoyed my plays of it, I'm not really certain that it will be a game that I will really think "I really need to play that" about, nor was I immediately motivated to start a new game after completing the previous one. I definitely wouldn't go out of my way to get a game of it in. I think this really starts relegating it to the filler category - something that you play because you want to play a game, and often that you're playing while waiting for a different game to be played (such as if several people in your gaming group are regularly late).
Overall, I give Babel an 8.0/10. I debated between a 7.5 and an 8.0, really thinking that this one isn't quite as good as Hive (which I also scored at 8.0). Eventually, I determined that I think I simply should have given Hive a higher score, as this one seems to fit in perfectly at 8.0 I think that it is a solid game, and would truly be ideal for someone looking for a game that they can carry around with them and teach whomever might be interested in gaming.