A game that I tried out based on a friend of mine mentioning it to me was Alhambra.
Alhambra is a tile placement game, similar to Carcassonne. In Alhambra, a player may choose one of three actions each turn: either they can take a currency card (or several as long as they add up to no more than 5), they can purchase and place a new building tile (which doesn't count against them if they spend the exact amount of money), or they can rearrange their alhambra (by removing a tile, adding a tile purchased on a previous round, or exchanging a tile). When replenishing cards after a player takes a currency card, a scoring card may appear which then will initiate scoring. Scoring occurs three times during the game - twice based off of cards, and once at the end of the game. When calculating scores, whoever has the most tiles of a certain type gets points (and in later scoring rounds, whoever has 2nd and 3rd most also get points). Finally, players also receive points for the longest exterior wall that they have built around their alhambra. At the end of the game (when no more tiles are available), the player with the most points wins.
The first thing that I like about Alhambra are the walls. The walls force a frustratingly delicate balance - they are worth points, so you want to connect a lot of walls, but they also limit your future tile placement, so you have to decide if it is worth it to seal off that part of your city. In one of the games that I played I wound up with a lot of exterior walls too quickly, and it caused me to not be able to place all of my tiles - but I was scoring 21 points for my walls. I like the delicate balance here, and it leads me to my next pro.
I like the tile placement rules. They are pretty intuitive once you are playing, but they can still be very limiting. One of the specific rules that can affect you if you wind up building a ton of walls is this: you cannot leave an empty square that you have built completely around. This caused me some frustrations during the end of our games because I ran out of places that I could put new tiles - I wouldn't be allowed to place them to complete my exterior wall until I had finished building all of the interior. And most of the interior pieces that were valid for me to play had already been purchased.
A point of note that's neither a pro nor a con is how currency works in the game. There are 4 different kinds of currency (represented by different colors and a small symbol) and 6 different kinds of tiles (represented by color and number of diamonds). When purchasing buildings, you base the purchase price on the number on the building tile and the purchase square that the tile is in (which shows the currency needed). I thought that how the different currencies worked was really neat, but I thought that the conflicting color coding was pretty confusing. I'm sure that if I keep playing the game, I will get used to it, but it takes an adjustment at first to know that I need to pay 4 blue for the green tile (and not 4 green) when it is on the blue space. Make sense, or did I throw too many colors around? If you're confused, then at least I'm not the only one.
With those pros, my biggest complaint with Alhambra is that it just didn't really excite me to play it. I'm realizing that I may be biased against tile placement games (I wasn't in love with Carcassonne either), but this game didn't really "strike my fancy." I could play the game again, but I could also not play it and be about equally happy. As a disclaimer, I will point out that we played the game two player, and we both agreed that it would probably be ideal to play with 4-6 players instead, and so you should factor that in with my previous comments.
After "much" internal debate (maybe 2 minutes worth), I give Alhambra a 7.5/10. I did not dislike playing the game (thus it does not get lower), but I'm also not itching to play it again. If you like tile placement games, you should check it out, because it seemed to be a good variant of the genre, but I think I will move on to other genres. I also gave it a bonus 0.5 because I think that it would work well as a game to be played with non-gamers.
If you like tile laying (unlike me) you might also want to read about Tsuro (this one is good enough I forget it's tile laying), and my favorite "traditional" tile laying game - Architekton. Or, if you're looking for games that you can play with non-gamers, you might read my review of Monopoly Deal or Sorry! Sliders.