Sorry if I mention things that others already have. Didn't read them all.
Poles for arena bad barrels and block to lift poles to make small jumps
Extra panels for a round pen
Pick nick table for lesson moms to chill at or whoever else wants to hang out
Hanging brushes bag for back of tack room door
Locks for tack room and feed room and multiple copy's of the key for boarders
Pallets to put hay on top of
Lots of tools so shovels, hammer, level,screws, power screwdriver , nails, crowbar, and lots of other basic tools that come in handy on almost a daily basis.
Box fans for stalls
Box fan holders
Caddy for soaps and such at wash rack
Cabinets to keep things like liniment, furazone , bandages etc.
Extra chairs if you decide to do something like a barn night. We have bonfire nights at the barn I'm at .everyone brings a dish and everyone hangs out eats, drinks and has a great time. There's usually more food than we can all eat and lots of laughs. Also helps to strengthen a barn family feel between boarders.
Automatic waterers if you want them
Hay storage area whether it's round or square bails you'll need a place to put them so some kind of covered awning .