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?
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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.