The Fire Country is the wealthiest nation, thus home to cities that are far more affluent than other countries. Obviously they renamed conquered settlements of other nations during the 100-year war (like Omashu renamed New Ozai). Most of the names are Chinese and mostly short (Hing Wa Island, Shu Jing, Jang Hui), but Japanese elements still exist (such as Kirachu Island). In this generator you can find both forms. This is similar to the names of the Earth Kingdom, but the Kingdom of Earth has two syllable names such as Goaling, Gaipain, Wulong while the fire nation has more two-word names such as those described before.
To generate another 15 random names you just have to press the button. With every click 15 new names are generated.
The Fire Nation Places are not really places of interests and have little to do with Avatar the movie. The place of the Fire Nation in the Avatar TLA is actually a lot more complicated than it seems at first. To start off, we will have to learn about the concept of the Avatar, and then we can talk about how the Fire Nation has been depicted throughout the history of Avatar. Then we can talk about why they were such a bad choice of villains for the film. This article will hopefully give you the information you need to make an informed decision.
The main character of Avatar was the daughter of Avatar Aang, who had lost his bending ability during the war. She was on a very long and difficult journey from the Earth Kingdom to the Air Nation, only to become treated like a prisoner in a very uncomfortable dress and shackles with terrible styles (to say the least). She also had gone through some very brutal battles with no respite at all aside from her short sitting time on a small ship that she had used to get to the Air Nomads. She finally made it to a Fire Nation city and after much struggle managed to escape from their grasp. The next time we see her she is in a prison in the Earth kingdom where she meets the Avatar, who has the same skills as her and also has a very bad reputation. In order to prove herself to the Avatar, she pretends to be the Avatar and helps him get rid of the Fire Lord and restore peace to the world.
If you do not want to go to this length, then there is no need to read the article all the way down to here, but if you really want to know what Fire Nation places are there are other resources out there. I highly recommend looking up the "Avatar the Last Airbender" series by Michael Dante DiMartino. It gives more information on the Fire Nation and the place that they rule and also explains why they are so evil in general. There are a few places where Avatar has a better villain than the Fire Nation and I would recommend looking those up as well, but I won't be doing any more of that here.