Given that this is a lore question, and not a specifically 5e one, I would strongly recommend the 2e product Forgotten Realms Adventures, as it has a section on 24 cities of the Heartlands with exactly the kind of information you are asking for. The catch with it is that a lot of the listed characters there are now dead (if you are playing past the Second Sundering). But even then, in terms of the social structures, most of the data are still remarkably intact. For each city in the FRA, the following information is provided: Who rules, who really rules behind the scenes, population, major products, armed forces, notable wizards, notable churches, notable rogues' and thieves' guilds, equipment shops, adventurer's quarters (lodging), important characters, important features in town, local lore and finally a small map.
As for the 3e, FR Campaign Setting (FRCS) is excellent. At 320 pages and with a small font, it is one of the most information packed D&D books ever published. (It received the Origins Award for Best Role-Playing Game Supplement of 2001.) It provides a decent amount of information on the cities, but not in the itemized format of FRA. Instead it has data on regions/countries and cities are given as individual paragraphs. So it covers a larger geography (significantly larger than FRA, or 5e Sword Coast Adventurer's Guide), but provides somewhat less detailed data on particular cities. One excellent thing in FRCS3e is a map of trade between regions.
The 4e Forgotten Realms Campaign Guide (FRCG) is structured in the same way as FRCS. However it lacks the level of detail FRCS provides. The 4e "Points of Light" philosophy is arguably reflected onto FRCG and the particular data on the cities are very limited. Moreover, 5e D&D (and the in-game mechanics of the Second Sundering) has mostly returned the setting to pretty much how it was in 2e/3e.
Finally, the 5e sourcebook Sword Coast Adventurer's Guide (SCAG) has partially returned to the style of FRA (cities are discussed explicitly), with a mix of FRCS3e. It covers more limited geography than FRCS3e, and the data on the cities is less organized than FRA (and some data are missing). Its main pro is that it happens to be the most recent published material. If one did not care about editions, FRCS3e and FRA are more suited to answer the question you have asked.
PS: Both FRA and FRCS3e are available as watermarked pdf downloads that you can buy on the web for less than half the price of SCAG.
I wondered this before myself, I found that Wikipedia had most of my answers.
The Forgotten Realms is a fantasy world setting, described as a world
of strange lands, dangerous creatures, and mighty deities, where magic
and supernatural phenomena are quite real. The premise is that, long
ago, the Earth and the world of the Forgotten Realms were more closely
connected. As time passed, the inhabitants of planet Earth have mostly
forgotten about the existence of that other world – hence the name
The AD&D 2nd edition Player’s Guide to the Forgotten Realms Campaign (TSR2142) explains on page 2 the name is based on its relation to our own world losing contact with and forgetting it:
What are the Forgotten Realms?
Some theorists explain dragons and other fantastic occurrences by postulating parallel worlds. In times past, they believe, travel between mundane worlds — like our own — and more exotic locales was easy and frequent. But we have lost contact, and lost the worlds themselves. Lost, or forgotten.
Abeir-Toril, more commonly Toril, is an Earth-sized planet dominated by a continent in its northern hemisphere. Called Faerûn in the west, it is here that the Forgotten Realms lie. […]
The Forgotten Realms is one of many D&D worlds, but it is not the default in any edition.
It's a common misconception that Forgotten Realms is the default setting for D&D. In fact, the "core" or "default" world varies by game edition, and in none of those is it stated to be the Forgotten Realms.
The closest is D&D 5th edition, where every single D&D world is officially considered to be part of a multiverse of all D&D worlds, meaning that the Forgotten Realms is part of the D&D universe, but no more so than, say, Eberron or Greyhawk. To quote Jeremy Crawford:
However, the Forgotten Realms is certainly given the most attention of any world in D&D 5e. It's the focus of the Adventurer's League organized play, as well as many official adventure modules. The ethnic groups of Faerûn are also the only ones described in the human race description in the Player's Handbook. This can give the impression that the Forgotten Realms is the "core" setting, but that's not strictly the case.
What was the core setting?
AD&D 1st edition had no default setting per se, and made no clear distinction between what was World of Greyhawk and what was "generic". When Forgotten Realms was introduced, many core or Greyhawk elements such as the Underdark and Great Wheel cosmology were simply included in the Realms.
AD&D 2nd edition did not focus on any one core setting, but had many settings. Sourcebooks for that edition often included sidebars for adaption to any of the many settings introduced in this edition of the game.
D&D 3rd edition made the World of Greyhawk the implied core setting. We see this with the deities in Player's Handbook.
D&D 4th edition detailed the Points of Light or Nentir Vale setting in the Dungeon Master's Guide, and that is considered its core setting.
D&D 5th edition includes numerous references to the Forgotten Realms, but if you read the Player's Handbook, there are also equal references to Greyhawk, Dragonlance, and so on. See my answer to Is Forgotten Realms the default setting in 5e? for my previous description of this.
Which world does each game inhabit?
The Forgotten Realms is a continuous and consistent setting. If you play a D&D 5th edition game, you are canonically inhabiting a world in which the cataclysms of AD&D 2e, D&D 3e and D&D 4e happened in the past.
However, the DM is entirely free to change any details of this, and in fact this is almost inevitable, since very few DMs have read every single Forgotten Realms sourcebook and novel, so their understanding of the world will naturally diverge. This is the normal state of affairs, according to the D&D 5e DMG p.4:
In other words, if my D&D group gets drunk and burns down Candlekeep, that event is only true within my campaign. In your campaign's continuity, Candlekeep may be fine and well. This is what is meant by "mirror universe". If you run a game set in the Forgotten Realms, it is your group's own interpretation of the Forgotten Realms.
Related to this topic, see Jackson Crawford's video When Myth Is Inconsistent.