I just paid 2000 caps for the home in Diamond City. To furnish the home, you need to build things in "workshop build mode", just like in settlements. As there is nowhere to put crops and water pumps, I gather that there won't be any settlers coming in, thus making happiness irrelevant? If true, it's a bummer. Even though this is the exact same thing we saw in the Elder Scrolls games, where we could buy homes and furniture, but after playing FO4, I want more. Now I like the sense of achievement from managing settlers and defense and improving happiness. Hope future mods would make it possible to have "roommates" as settlers and burglars as attackers (though it would be awkward to put 20 turrets in the living room).
Another interesting thing is that this Diamond City home is the only "settlement" located behind a closed door, thus separated from the main world. All other settlements exist in the main world itself, where any locations in separate areas (such as the basemant in Croup Manor) are not part of the settlements.