New Atlantis is both the first city that you visit in Starfield and the most boring one. The best cities to visit are elsewhere in the galaxy, offering characters and missions with cool vibes. New Atlantis, however, is like getting lost in an sterilized sci-fi parking lot.
Starfield's cities are so distinct that it's best to think about them like choosing your character backgrounds. The missions and people in each city let you decide what kind of character you want to play and what kind of themes you want to explore within Bethesda's new universe.
Major cities are home to the major factions in the world, like the Freestar Rangers and the UC Vanguard, and smaller cities, like Cydonia, have missions that help illustrate what it's like to live on the outskirts of the main systems. Choosing a city to start with is the best way to jump straight into storylines you're actually interested in rather than tediously clearing out activities you don't really care about.
Here are the Starfield cities worth visiting first (after you get out of New Atlantis as fast as you can) and what sort of missions you'll find there:
Location: Volii Alpha, Volii system
Factions: Ryujin Industries, Xenofresh Corporation
Neon is as close as you can get to cyberpunk in Starfield. Massive, flashing signs light up its streets as crowds of people hover round its nightclubs and shops. It's the kind of place you go if you want to party or make an illegal drug deal or two. Here you can break the law and take on missions that might get you mixed up with the local gangs. Neon won't make a lot of your Constellation friends happy, but it's the place to go if you want to meet Starfield's shadiest people.
Location: Akila, Cheyenne system
Theme: Fallout/American West
Factions: Freestar Rangers
Starfield has an entire city that would fit just fine in a Fallout game. There aren't any ghouls, but there are people who abuse the hands-off approach of the local government, the Freestar Collective. In Akila City, you can join the rangers and hunt space bandits or the dangerous Ashta aliens. It's not surprising that you have to stop a bank robbery as soon as you arrive: This is the city to visit if you want to be Starfield's version of a space cowboy.
Location: Suvorov, Kryx system
Theme: Space pirates
Factions: Crimson Fleet
The Key requires you to finish a chain of missions before you can safely enter it. You need to either get arrested for holding contraband or something worse, or start the UC Vanguard faction missions in New Atlantis.
Once you're friendly with the Crimson Fleet, you'll be able to enter the space station and meet a variety of pirate captains. In The Key, you can make loads of credits selling contraband, or help the Crimson Fleet infiltrate and battle with the UC System Defense division. This is the most criminal Starfield cities get, so only chill here if you're down for breaking the law every chance you get.
Location: Mars, Sol system
Theme: Mining town
The oldest colony in Starfield dug into the center of Mars and decided to live there. Cydonia is a sad place where everything seems to be falling apart. The people need help with everything from alien infestations to familial disputes. You won't find a faction in Cydonia, but you'll find several quests that make you feel like you're doing the right thing and helping out one of the roughest places in the galaxy.