Living with an urban planner, I play a lot of city-building and tile-placing games. One we particularly like is Suburbia. It has a good combination of flexibility, strategy, and chance.
Each player is building their own little borough from four categories of tiles: residential, commercial, industrial, and civic. Tiles can have different effects depending on adjacent tiles, other tiles in your borough, or sometimes even tiles in other boroughs. For instance, there might be a penalty for putting heavy industry next to a school, or your restaurant could lose income when someone builds a newer, fancier restaurant. Tiles are available via an auction system each turn.
As a developer, your moves are a delicate balance of attracting a large population and maintaining a high income without losing reputation. (Building a casino may bring you a lot of income, but it costs you a lot of reputation points, which affects your population.) However, as you advance up the population track (aka the scoreboard), you lose income and reputation. This means that on some turns you may not want to collect too many points.
There are a set of public goals for which all players can compete. In addition, each player has a personal goal they are trying to achieve, but this goal is hidden from other players (and could even be in conflict with the public goals). Goals will add population/points at the end of the game.
Suburbia is a good mix of strategy with a little bit of luck (not all tiles come out each game, so there’s no guarantee your investments will work out). The diversity of goals make for a different game each time. There is enough going on to stay engaged throughout the game, but not so much that it’s difficult to learn.