Taken from Wikpedia:

No building or apartment in Seattle really has the view from Frasier's residence. It was created so the Space Needle would appear more prominently. According to the Season 1 DVD bonus features, the photograph used on the set was taken from atop a cliff, possibly the ledge at Kerry Park, a frequent photography location. Despite this, Frasier has been said to have contributed to the emergence of an upscale urban lifestyle in 1990s Seattle, with buyers seeking properties in locations resembling that depicted in the show, in search of "that cosmopolitan feel of Frasier".

As mentioned on my CafeNervosa yahoo group. I always thought the picture was taken from Kerry Park!!!!;)

Sadly that's true that no one has that cool view, but I've been to Kerry Park and it's awesome; just a different perspective of the skyline than you normally see. In actuality, the Space Needle is at the "end" of the skyline but Kerry Park makes it seem like it's right in the middle.