I'll throw in my two sense just for shirts and giggles.
First, I would be forced to question why you can't run cat5 cables in the building... If you're doing this as your own pet project I can understand, but it sounds like it's the sort of thing that's sanctioned by the building owners. Running cat5 in buildings, at least to the riser rooms is usually disgustingly easy. You'll already have demarcation from the last mile provider likely in a riser room, so I would obviously question why this is a problem... Riser rooms are typically one on top of the others with cable pipes already installed, so you don't even need to be an expert at fishing.
That said, you can still run various wireless systems, you'll just have to do some sort of point to point wireless distribution system (which you would need anyway). Many of them rely on the access points being hard wired in, but you can still get away with not. What you're looking for is a business grade wireless system that supports peering, repeating, etc. Beyond a handful of access points, you typically want to run a wireless controller of some kind (that centrally controls and manages the whole gambit of AP's). D-Link has a variety of products in this area that aren't too expensive (read: Cisco 4400).
Throw that in with a router of some kind, perhaps one that supports a captive portal (as soon as users connected and open their browser, they have to enter in a username/password to 'connect'). With a captive portal you could then control access to the system very easily. You might also want to look at a router that supports traffic shaping of some kind, so your building's P2P users don't totally flog the connection. You can do all of this for free with something like pfsense (the most popular Linux/BSD based router software - free, easy to install, easy to manage (no command line), and has the features of a $3000+ router). But you'll want a router that supports some features like this. Honestly, pfsense would fit the bill perfectly here (you can run it on just about any hardware).
Personally, I've done a few systems like this, but typically with much higher end gear (Cisco 4400 controllers - about $12,000 a pop). But I've 'seen' a few places that have a slick D-Link setup and it really is slick. The Cisco stuff is slick if you have a budget ($20 - $50K). Mosey on over to D-Link website and have a look at some of their business grade gear, specifically their wireless controllers and that'll start giving you an idea of what you're looking for.
If you're on a super-non-existent budget, you can try getting a boatload of WRT54GL's and putting the alternative f/w on them. I've heard of a friend doing this for a roughly similar setup and supposedly it worked decently (although he's always replacing a dead WRT).
