Jim,  Hmm, an interesting question, as it really depends on what
you have on hand and how much restoration work you are going to do.
A one-time restoration of one's own player is one thing, and you can
get by with a limited amount of tools.  If you are going to do a lot
of pianos, well, then you'll need a lot of tools.

With that in mind, besides the normal assortment of hand tools
(screwdrivers, pliers, wrenches, nut drivers, drills, etc.) there
are some basic woodworking tools I find useful: a good drill press;
a combination disk/belt stationary sander; a table saw with a _good_
fence, and of course an assortment of _sharp_ blades.  I have a Jet
10" table saw that does nicely (but I also use it for other projects
like building shelves, remodeling the house, etc. so I can justify
its purchase).  These tools are all used to repair or replicate
pneumatic wood pieces.

A polishing machine with an assortment of buffs and buffing compound.
I also now have a metal lathe that I have used to turn parts.  The
oddest use I put it to was recently turning some wood chain tensioner
pulleys!  Yes, this would be a luxury item; I have it to make parts
for old cars, toy trains and steam stuff, and I got it _cheap_ from
an estate sale or it wouldn't be in my shop.  I doubt I have used it
enough to justify it except for the fun it has given me.

Now for really specialized stuff: an adjustable vacuum source for
testing; a low-vacuum gauge that reads inches of water instead of
mercury; if you shop around you can find one inexpensively.  I also
have an Auto-Pneumatic gauge I bought at a yard sale decades ago.
Why they had it no one knows -- they didn't know what it was.  They
had nothing else piano related!

I also have a mini heat gun and a full-sized heat gun for ungluing
stuff and un-warping wood, and a glue pot (I'm cheap, it's actually
a crock pot!)

Now I don't have this, but if you have the space, multiple working
benches so you can have different projects going on at the same time.
This allows you to be doing other stuff while glue is setting up, etc.

Oh yes:  Clamps -- lots of them!  One can never have enough clamps.
Well, okay, one can, but...!  Oh, and good lighting.

And then there's the really specialized tools, pouch setters, pneumatic
span gauge, leather nut driver.  I'm probably forgetting something!

I do have one other very specialized thing: a Caswell brush plating
nickel & copper kit for replating small parts, like wind motor
crankshafts.  It doesn't happen to every player, but it does happen.

Now if you're doing only one piano, a glue pot (mini-crock pot from a
thrift store), span gauge and pouch setter will get you by if you have
the hand tools and lots of patience.

Oh, a metal straight edge is also very useful, and good cutting tools
(scissors, X-Acto type knives, single edge razor blades).

Okay, I'm standing back to see what other responses you get!

David Dewey