Board Design Problems

I usually favor modular boards, as long as they work well thematically and visually. It is a bit more work design-wise, but they tend to add replayability to the game, hence the extra work is not in vain. And based on my experience, most players like tile-based boards, so that is a plus.

Depending on how the game is played and what suits the game theme better, you can either have a map setup phase at the start of the game, and then play as with a predefined map, or have the tile placing as part of the players turns (in which case, it might be an integral part of each player's turn or just one of the available actions).

In any case, I think, as long as the game allows, a game board based on tiles is usually a good thing.

I also like the modular approach, if it makes sense and it makes the game more interesting.

In Betrayal, the players are exploring a haunted house that they've never visited before, so it makes sense that they are discovering each new room. In your game, if the player are residents of the city, then it doesn't make sense that they don't already know the layout of the city. If that's the case, you might still use a modular approach, but have them lay it all out in advance.

The other way that Betrayal uses this mechanic well is that there are actions that tell you to go to a particular room, or to one of several rooms. With the slowly-revealed board, those rooms might not yet be on the board. Even if they are already revealed, how near or far they are is unpredictable, in a good way. Of course, that means that the need to get to the named area can't be too crushing, or it becomes imbalancing. If your areas have names and reasons to visit specific ones, to get a smallish benefit or to wipe out a smallish detriment, I think it could add to the variety and fun of the game.