When trying to think up names for Sim City 4 cities or fantasy football team names or for any of many others reasons why someone like me might want to make up place names, Gotham has always been a thorn in my side. No matter how hard I try, I cannot think of a name as good as Gotham. Part of that is probably because it is so ingrained in pop culture and my mind that it actually feels like a real place and actual names always seem more realistic than fake ones. Moreover, the fact that Gotham is actually a nickname for New York probably gives some added weight to it.
Still, the name is simply perfect. It is short and catchy, yet manages to evoke so many images. Goth elicits memories of barbarian tribes, towering Gothic cathedrals and darkness, while ham is a simple English town ending. Thus, it manages to be a reference, but still sound like a real place.
But because Gotham is not a honest-to-goodness physical place, the most important part of its reality is in the mind. Gotham is darkness, it is madness, an art-deco nightmare. It is shadow, towering skyscrapers and muggings on street corners. When you think of Gotham City it brings to mind images of a real place, just as if you thought of New York, London or Hong Kong.
I haven't been able to find quite as much information the geography of the city itself, but I did find some interesting things.
Strange Maps, which actually began this endeavor, has a post with some information on various places in the city, as does
Gotham and Beyond. I'm not well versed enough with comics to comment further on those particulars, so let's just get to the maps.
The first image comes from Batman: The Animated Series, and honestly isn't all that helpful. Though it's a nice sepia tone and I just like the way it looks.

This next map is the original from Strange Maps and wonderful for city details, but not great for larger area names. As far as I can tell Gotham City is comprised of three main islands, two secondary islands and a few other islands here or there (including Blackgate Isle, #41 on the map). The islands I consider secondary are the two triangular ones, the northern containing Arkham Asylum, the southern the Tricorner Yards. These seem very integrated into the city and important, with an expressway going through the northern and the shipyards on the southern. The other islands are not given much detail, only showing a few bridges connecting them to the main islands and one road.

Here is a subway map of Gotham, which gives some nice detail on neighborhood names. It also gives us the areas of Uptown, Midtown and Downtown (obviously modeled after NYC), but no names for the actual islands which these areas of the city are on. A non-subway map similar to this can be found
here. It has a zoom function, lists all sorts of street names and is without a doubt the best map of the city I have found. Oddly, both of these maps get rid of four of the five islands in the south of the city.

From these maps we get the following neighborhoods.
Uptown: Granton, Farrow, Harrow, Jerold.
Midtown: Gainsly, Reatton.
Downtown: Haysville, Stevensburgh, West Harlow.
Additionally, there is the Narrows between Midtown and Downtown, and the island in the southwest corner is South Hinkley.
I would appreciate any input those readers with more comic book knowledge than me have.