Ideas for wiring an apartment building for wireless (multiple nodes)

Although it works, cascading switches leads to possible poor performance down the chain. Everyone on the fourth floor is sharing the uplink to the third floor, the same goes down the line... In addition to that, this introduces more points of failure. If the switch on floor two fails, everyone from 2-4 loses their connection.

Hire a professional technician to wire all the floors to a patch panel in the basement. That way you can have one switch to manage all the connections. This makes life much easier.

The first thing I'd do would be to get rid of the daisy chained switches, and have each floor feed into a master switch. This would ensure that every floor has the same amount of network hops to the router, and any network faults doesn't split the building in two.

Seeing as you already have a switch in the basement, this could be used as master switch, provided that you have enough ports, and that it has the capacity. I wouldn't go for anything less than gigabit here).

From the way I read your schematic, each switch has 3 wireless routers attached to it. Consider using these as access points only, so that the entire building is on the same subnet. Alternatively, one subnet per floor. This would allow for easy interaction between computers across floors.

To give a solid answer, we'd need more specifics. How tall is 'terribly tall'? Ideally, you'd take the building's drawings/blueprints and map the planned runs to determine length. How many wired clients do you estimate?

Based on what you've said, I'd estimate that you need just one switch in the basement with Cat5 or Cat6 run to each access point location. A properly terminated and tested 300' cable run will work just fine, and having only one switch sounds much more desirable in your situation, since you will only have to buy, manage, and eventually replace one.

You also need to either research local codes or hire a professional to avoid creating fire hazards. At a minimum, you need CMR-rated (CoMunications Riser) cable for vertical runs. Some codes also require conduits and/or fire stops.

Alternatively, if you must have switches all over the place, consider connecting them back to the central node with fiber. It's a little trickier on the front end but allows for very long runs and is less prone to long-term issues like lightning and corrosion. Fiber's also dirt cheap these days.

If you're dealing with 50mbps, the gigabit Ethernet is extremely unlikely to be the cause of the current setup's problems. (Presumably it has some, or you wouldn't replace it or call it crappy). You should mostly focus on getting the radios right: make sure there is good signal strength & SNR throughout the building, channel overlap minimized to the extent possible, etc.

I think the ideal layout for your network would be to have all 12 access points wired to a patch panel in the basement, all connected to one switch. (If that's not doable because it'd require cable runs > 100 meters, then a 2nd switch on the 3rd or 4th floor.) The main advantage there is that you can troubleshoot from one place (no more running between floors to check link lights), you can use one UPS to provide backup power to everything, and it's easier to manage one switch instead of 5. You also have fewer points of failure.

But I'd definitely spend the budget on improving radio coverage first.