Early on in the game you'll be invited to place a house for the Mayor (You!). Personally, I like to plop this in the more difficult residental areas due to the positive effect it will have on the surrounding houses. But it's not the only residence you'll get. Later on you'll get invited to add a Mansion for the Mayor, now this house is more interested as it comes with numerous upgrades and like the City Hall, will need a sizeable plot. Like the Mayor's House, I like to plop the Mansion in the more difficult low-wealth residential areas, to try to bring them up. It's pretty easy to get the central residential zones upgrades, but the ones on the outer parts of the map are sometimes more difficult and can benefit from having the Mayor's residencies close-by.
As you achieve certain things in the game, such as a happiness rating of 75% or more for 6 hours you'll get awarded with the option to add various upgrades, they may seem a little pointless but they have a positive effect on the neighbourhood and Sims seem to like to see the Mayor doing well for himself.
Mayor's Mansion and House
The screenshot above shows the Mayor's residencies these have been plopped closed to a difficult residential zone which is not so attractive as it is close to the rubbish dump, recycling pland and industrial zones.