Akropolis

In Akropolis, each player builds an ancient Greek city out of hexagonal tiles. On your turn you take one tile from a shared row (the further along the row, the more it costs in stones) and add it to your city. Tiles can be stacked on top of others to build upward.

Each district type (houses, markets, barracks, temples, gardens) has its own placement rule, and districts score more the higher they are built and the more matching plazas you have. It plays in about 30 minutes, is simple to teach, and still gives a satisfying puzzle each game.