Up to you what to label. I wouldn't label it if you don't think it is important information when looking at the map (for instance, you don't have to label the main post office if it doesn't play a part in what you want people to see on the map). Although, to your point, since it is a large city, I would label both (but that is opinion, which you can ignore, no hard feelings ).

If you want to label both there are a bunch of ways to do that. First, you could change fonts (although I like the one you made) if you want to label the districts separately from the buildings/landmarks.

Or you could make the font bigger, but slightly transparent for the districts while the buildings/landmarks are smaller font, but full opacity.

If you don't like either of those ideas, you could have a border, do a dark outline/light outline, or some combination of the two to make the districts or the building/landmark labels pop (see here for an example of someone going through this exact situation right now: https://www.cartographersguild.com/s...ad.php?t=46502).

Alternatively to all of the previous ideas, you could label the districts themselves with full opacity labels (border and highlights up to you) and then number the buildings/landmarks with a title/description (city hall, park, library, etc) for each in a key/legend beside their corresponding number.