Learn Dutch: De koning heeft verschillende steden bezocht, waaronder deze oude vesting. - The king visited various cities, including this old fortress.

Waaronder is a relative pronominal adverb made of waar (where/which) + onder (under/among). Literally meaning "under which" or "among which", it refers back to the plural group verschillende steden (various cities). In Dutch, it is the standard way to express "including" when giving a specific example from a previously mentioned group.

Is waaronder acting as a relative pronoun here? If so, where is the verb at the end of the clause?

It is a relative pronominal adverb, which normally sends the verb to the end of the clause. However, this is an elliptical (shortened) clause. The full thought would be something like waaronder deze oude vesting valt (under which this old fortress falls), but Dutch naturally shortens this to just waaronder plus the noun phrase, just as English does with "including".

Could I use inclusief instead of waaronder?

You could say inclusief deze oude vesting, but waaronder is much more common and natural in Dutch when singling out a specific item from a broader category. Inclusief is usually reserved for pricing, packages, or bundled items (e.g., a hotel room inclusive of breakfast).

Why does the adjective oude get an -e ending here?