Other than the city center, what decides whether an adjacent district is included within the city walls? Are there factors to consider when building a city to ensure that a higher elevation tile adjacent/close to a city center gets included inside the walls, so I can avoid AI using the high ground to siege a city?

Every chain-adjacent to Main Plaza district is inside city walls. 

Not included districts could be:

- remote districts (like luxury exploits) 

- districts attached to administrative center which is not chain-adjacent to Main Plaza.

There is a caveat : garrison disctricts are considered fortified as well. Not exactly city walls, but it can be usefull.

Also, ruins district (for example, district that has been destroyed by bombardment) will have destroyed fortification even if inside the main borough.