The general list of features you should consider has been pretty well covered by others, I will tackle this from a slightly different angle:

Just how important is the camera to you?

Is it more or less important than the phone features, or the phone OS for example? There are options that prioritize the camera over the phone, like the Samsung Galaxy S4 Zoom. It is more of a camera that happens to be a phone than a phone that comes with a camera. The zoom gives you 10x optical zoom and a friend of mine that attended conferences a lot and blogged absolutely loved it. Personally, I found it a little too bulky and I would prioritize other things.

If budget is no concern, but you don't want a dedicated camera, you can have your normal phone camera for most things, and then get a QX100 or similar (QX Series) from Sony that gives you a Carl Zeiss lens and separate sensor independent from your phone.

Then you get clever attempts to make digital zoom not suck, like the Lumia 1020, which gives you a 2.7x zoom equivalent at 5 megapixels.

The general list of features you should consider has been pretty well covered by others, I will tackle this from a slightly different angle:

Just how important is the camera to you?

Is it more or less important than the phone features, or the phone OS for example? There are options that prioritize the camera over the phone, like the Samsung Galaxy S4 Zoom. It is more of a camera that happens to be a phone than a phone that comes with a camera. The zoom gives you 10x optical zoom and a friend of mine that attended conferences a lot and blogged absolutely loved it. Personally, I found it a little too bulky and I would prioritize other things.

If budget is no concern, but you don't want a dedicated camera, you can have your normal phone camera for most things, and then get a QX100 or similar (QX Series) from Sony that gives you a Carl Zeiss lens and separate sensor independent from your phone.

Then you get clever attempts to make digital zoom not suck, like the Lumia 1020, which gives you a 2.7x zoom equivalent at 5 megapixels. For that though, you have to be OK with Windows OS versus Android or iOS.

Finally, I am loathe to point you at something that is not available at the time of writing (but it is expected within the next month or so), but the Asus Zenfone Zoom seems like it may hit a sweetspot - 3x optical zoom, still slim, Image Stabilisation support, Android OS, and more.