concrete (cinder) block tower with wood chopping block for turntable stand

One can spend the money, expend the energy, or do a bit of both....
It can be many things, functional, practical, pricey, cheap....

As long as it does what you think and/or feel you/'It' needs....:)

I put mine on the concrete slab floor.

should be fine.  add some iso-acoustics isolators if you need to, or continue in the diy mode and place a simple cush-pad under the turntable like is used for floors... you can buy a couple feet off a roll at home depot, it's grey rubbery material and actually works pretty well as vibration isolation... cut a 16'x16' square and place TT on it, or four 4'x4' squares just under the feet of the TT.  If you need to... try without, first; most TTs these days (and even decent ones from 30-40 years ago) have pretty good vibration isolation already  

" cut a 16'x16' square and place TT on it, or four 4'x4' squares just under the feet of the TT. "

Just exactly how big is this turntable??!!

Might look up these guys:

https://skyfiaudio.com/products/bright-star-audio-sand-filled-isolation-platform-with-air-cushion-and-pump

Happy listening.