It depends what you mean by "inner west". There's the fashionable suburbs of Newtown, Erskineville to the up-and-coming areas like Marrickville and St. Peters. The north-of-parramatta areas like Leichardt, Haberfield, Annandale will always be the more prestigious end of the inner west and family-oriented.
We used to live in Stanmore and Marrickville and loved it. Except for the planes in Marrickville (Although many have noise insulation and air conditioning). We would have stayed in Stanmore if we could afford to buy. It has a very established feel to the area.
Coogee is Coogee. I don't know the area very well, but it seems nice.
In addition to all the good comments on land values, placement to schools is going to be a long-term deciding factor for family areas. Trinity Grammar (Summerhill) and Newington Boys (Stanmore) are two very highly rated public high schools in the Inner West. They are a moderating effect on prices. The prices may get stupid, but the inner inner west will never become unfashonable (IMHO, hope I don't eat my words
).
Some inner west suburbs have a 20xx post code and others start with 22xx. And that makes a difference in people's perception. Newington Boys obviously sits on the Marrickville(2204) side of Stanmore Road, but suburb boundary line does a BIG detour to include it in Stanmore (2048). If you're not sure what the fuss is, 2200 is Bankstown. Shudder. So like I said, it depends on which part of the Inner West.
Mind you, if you can get land, then that is the better choice from an investment point of view.
You may also get a better chance at long term, professional tennants in the Inner West as well.
My two cents.