The Hill Giant is Huge (occupies a 15'x15' space). It has a Greatclub weapon attack with reach 10'.
What is the Giant's unarmed reach? What is his reach for grappling?
The reach keyword only applies to what the stat block attaches it to, in this case the greatclub.
There is no description of a Hill Giant's unarmed strike (you could certainly homebrew one) so it would follow the default rules:
Most creatures have a 5-foot reach and can thus attack targets within 5 feet of them when making a melee attack. Certain creatures (typically those larger than Medium) have melee attacks with a greater reach than 5 feet, as noted in their descriptions
Grappling follows the same restrictions as it counts as a melee Attack action.
Grapple is defined in the PHB as a "special melee attack"
When you want to grab a creature or wrestle with it, you can use the Attack action to make a Special melee attack, a grapple.
A greatclub has a standard 5' reach so we can assume that the bonus to the greatclub's reach comes from the Hill Giant's natural reach rather than just a really long greatclub. Therefore, I would assume that the Hill Giant has a 10 foot reach with all melee attacks, including grapple, due to it's natural large size.
But you can rule it however you want. Maybe it has a 5 foot reach and a 5 foot long great club. If you're the DM, it could go however you wish. Trust your instincts, but the former is how I would rule it.
In Storm King’s Thunder, on page 50, under the "Defense of Goldenfields" subheading of the "Attack on Goldenfields" section, there is an unarmed Hill Giant’s statistics:
If forced into melee combat, an unarmed hill giant can use its action to make two unarmed attacks. Replace the giant’s greatclub attack with the following attack option:
Unarmed Attack. Melee Weapon Attack: +8 to hit, reach 10 ft., one target. Hit: 12 (3d4 + 5) bludgeoning damage.