This is certainly Rainbows End by Vernor Vinge. It matches pretty much point for point.
The guy brought back from Alzheimer's is the main character and the story deals with him coming to grips with a new world much nearer the Singularity than what he last remembered. He was a poet and prior to his Alzheimer's didn't have a technical bone in his body, but after coming back, his mind seems improved and he now has new technical skills as well.
The computers-in-clothing gives him a bit of trouble, but he decides to adapt and learn the gesture language used to control them.
The other protagonist as an AI who is lurking in the sidelines and seems to be generally helpful, if occasionally prone to bits of mischief. (Like leaving carrots that can't be removed on people vistual desktops.)
(Two other great scenes: One, when the AI walks the UCSD Library building and the other where the cyber security agencies discover the AI and try to kill it by revoking root certificates.)
The underground part is when his granddaughter -- I think -- is taken by terrorists and held in an underground (literally) lab in San Diego. The US military used orbital lasers to melt into the lab and the good guys are saved.
It's a brilliant book by one of the masters.