Where do you store your pistol cleaning kit?
I found a big tackle box at a thrift store for $5.00 that holds all my cleaning gear and spare parts and tools. 
.50 cal ammonia box.
What cleaning kit? 
I have an Otis kit. It’s self contained. It is stored in a drawer at the bottom of my gun cabinet.
My Otis kit is the size of a large bran muffin. I just carry it in my range bag, along with Sig’s Spec1 Combo Pack in a ziploc.
Went to Walmart and bought a ammo case for 4.88 and that’s what holds my firearm cleaner and all brushes etc. 

In my USCCA range bag.
In a storage tub in side an old refrigerator in the garage next to my reloading bench
I use the Tackle box. I have the tools all organized by the sizes and big storage space on the bottom for the CLP, grease, solvent. and degreaser. My ultra sonic cleaner is in the war room at the far end of the room from my reloading press.
Brush, towel, and oil. Like a day at the beach! 
Plastic shoe box with buckle type latches.
^^^^ What Enzo_T said
Since building my reloading room I found it much easier to use the bench in there to clean/inspect so I keep all of my cleaning supplies in there.
All in one 12 quart Rubbermaid latchables container.
I have a small tool bag that I use for it. Easy to transport as needed. I only have a small kit right now and only have handguns. I am sure as I add to my assortment my cleaning needs will grow as well.
@Brad great minds think alike. I use the same thing.
I only have to support three handgun calibers: .45, .38, and .22
Shotgun and rifle cleaning kits I keep separate because of the length of the cleaning rods and they don’t see near the amount of use.
With the current ammo unpleasantness, none of them are seeing much use!
Tackle box for most of it. An empty six pack carton for the oils and spray cleaners. Doing my part to be green… 
Same set up

