Setting - generic or name that city?

If you can get through the story without naming the city, and it is not obvious that you are hiding the name, then, I'm guessing it would be all right.
On the other hand, even big cities have neighborhoods, If you describe a real neighborhood, using street names, restaurant names, etc., you will be giving the city's name away to those familiar with the neighborhood.
In my stories, I name the city (Niagara Falls) because the landscape plays a part in the stories.
The WIP I started recently, takes place in the suburbs of Buffalo. The location isn't important, other than it is familiar to me, making it easier to write.
Because I use real cities & towns, I change the names and addresses of any businesses where action takes place. That way, no one can point a finger, saying I hurt their business.

I'd name the city, even if it's a created name, honestly.

To say "I drove into the city" would put NYC instantly into the minds of many East Coasters, but put LA into West Coasters heads and who knows what other parts of the country/world would automatically expect out of the book because of this vague reference. This could easily lead to confusion, then dissatisfaction on the part of the reader for un/subconscious causes.

No sense in taking a risk for something that's so easily fixed.

If it happens to come out naturally in the story, name it. If not, don't worry about it. And you'd probably only need to use a real name if the location or landmarks were important to the story in some way. If they aren't, a made up name in real state/country is fine. The only time it would probably matter is if you claimed it was X and used landmarks but got the facts wrong.

I kept mine generic, but I was going for a certain feel. I wanted the city to be a character unto itself, and I didn't think I could do that if I were to give it a name.

It depends. If the story dictates the story to happen in a specific place (for example, King Kong in New York climbing the Empire State Building), then you should use the real location and name it. If it's a made-up place (Gotham or Oz), you still should name it. But if it's really generic (just some town in middle America), then you can probably get away without naming the town because the story doesn't require it -- the location is not important at all.

For verisimilitude, it's probably a good idea to at least mention the location. Often people talk about where they live, etc. and the name of the town or city or state or country grounds your readers (even if it's just some made-up town called Springfield!). When the location is completely generic (Fifth Street and Main), it loses a bit of realism, I think...

My short stories, for example, tend to be generic, because the location simply doesn't matter. For a novel, however, I wonder if we can avoid naming the specific town/city throughout the whole book. I guess it depends on the genre. Mystery could probably get around it -- as long as there's a downtown, the north side, the east side... sometimes that's all you need.

My story is based on a real town and real corruption. I changed it but I hope people think they know where it is. I just won't admit to it.
Jane

Give the area it's in:

A Northern town in England
A small town in the Deep South.

Well for me I've set my novel in Newcastle (UK) mainly because it's my home town; also because I get to mix the gothic medieval city that lurks in the recesses of the neoclassic Victorian city centre and the cosmopolitan regeneration of the last 15 years.

For me, I couldn't create anything better myself.