Start with a game board piece with low development costs. That way, you will have more money available for your service and utility buildings.
Use the opportunity to exchange construction cards. That will let you save cards for later that can't help you at the moment.
Try to construct utility buildings at the edge, where they won't bother anyone. You can also try building them in still-empty districts, thereby gaining the prerequisite for ending a Milestone.
In the "Stage I" cards, you will find the simple, inexpensive service buildings that have benefits that you can use right away. Of course, you will have to be sure to build the zones directly adjacent to each other.
Therefore, build them in such a way that you can add adjacent zones on many sides. Keep in mind that they can also be used for an adjacent game board piece once you play the next Milestone.
It is best to draw "Stage II" cards early. There, you will find service buildings that will impact the entire district. You do not have to build them centrally, and when you add an adjacent game board piece they will have an impact on the larger district that results.
You should only take "Stage III" cards after you have already built some things, and have more money in the treasury.
Pay attention to the bars for pollution, traffic, and crime. Even if it is not until the end of the game that they will have an impact on overall Happiness and thus on the final result, you should keep an eye on them throughout the game.
If their values reach the limit, you cannot play any cards that would raise them, thus restricting your possibilities.
Since most of the game board pieces only consist of three or four city districts, a Milestone can often be completed very quickly. If, however, the values on your administration board are too low, you might end up losing a lot of Happiness or paying money due to your employment bar.
In that case, it would be better to try to improve these values rather than ending the current Milestone right away.
Each increase in Happiness will yield multiple benefits, since the attained value also counts for later Milestones.
Be sure that you still have enough money in the treasury for the next Milestone. You will have to be able to pay the development costs for an adjacent game board piece. And you also should keep enough money to be able to build new service and utility buildings.