I have a 1986 corvette that had been sitting in a New York city parking garage for over 25 years. It has bilstein shocks. Do you think those should be replaced?

Probably a good idea, as the valves inside the shocks are dried out, due to lack of movement of the internal fluid. Changed mine a few years ago, quite a difference in handling and comfort. Check out RockAuto and suppliers like that for deals. Some of the Corvette guys (Eckler's) run specials sometimes.

Absolutely.

There's going to be a handful of 36y/o parts that need replacement to be road worthy.

Yep, my experience is almost everything rubber needs to be replaced and a lot of plastic parts in the engine compartment probably should be replaces too.  Tires, belts, spark plug wires, hoses and such over about 15 years old are starting to go, tires should be replaced as 6-7 years just due to age.  

Some of the rubber and plastic can be replaced a little at a time as they fail and you are working in that area.  But major rubber and plastic parts that are part of the driveline need to be replaced!  I have replaced some parts that were replaced before because they are going bad again!  These cars are 30-40 years old.  They just look like a new modern car, but the are truly antiques!  Rubber and plastics go bad with heat, age and sunlight!

Totally agree ... just replaced shocks in our 83 ... didn’t really need it but you know - think it’s a good idea every 37 years whether it needs it or not.