I am looking for information about the main cities in the Forgotten Realms for developing a backstory. Are there any resources out there that compare what makes one city different than another? What makes Silverymoon or Baldur's Gate different from Waterdeep, Luskan, or any other city.
Any information like government style, dominant religions, dominant races, presence of organizations like thieves guilds or mage guilds, or even the climate these places have would be useful.
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.
Yes, such resources do exist:
Sword Coast Adventurer’s Guide is a great way to catch up on recent events in the Forgotten Realms, to get background on locations featured in the Rage of Demons storyline coming in September, and to learn the lore behind video games like Neverwinter and Sword Coast Legends.
Immersive Adventuring: This campaign sourcebook provides players and Dungeon Masters material for creating vibrant fantasy stories along the Sword Coast.
Adventure in the Forgotten Realms: Discover the current state of the Forgotten Realms and its deities after the Spellplague and the second Sundering. You’ll also get updated maps of this area of the Realms.
Insider Information: Learn the background behind locations, such as Luskan and Gracklstugh, featured in the upcoming digital RPG, Sword Coast Legends.
The book goes into detail about the story/main events relevant to each city, talks about neighbors, allies, enemies, and notable characters.
This info applies to FR as described in 5E, which is the most recent state of things, so to speak. Nothing prevents you from adapting earlier epochs in the FR; in that case, though, you would have to look into older books.
The Forgotten Realms Wiki has an absolutely staggering amount of information about everything in the Forgotten Realms.
This includes Category:Metropolises , which has writups on over a hundred cities with a population larger than 25,000, including Silverymoon, Baldur's Gate, Waterdeep, and Luskan.
While sourcebooks of earlier editions have a wealth of information on many cities, the Forgotten Realms Wiki has the advantage of being more readily accessible to many people.
I have quite recently read the Sword Coast Adventurer's Guide, and have found it to be detailed enough to, with no other prep and no improvisation, do nothing more than a brief, flavourful passing through. However, after coming up with an inn at the right price-range for your players and a couple of market sellers, fitting into the stuff the book talks about, you can then create a detailed and pleasant experience for your players.
If you are in the market for something free, then I am not really sure, but I would advise you search for Wikis etcetera.
