It's really a matter of subjective opinion, isn't it? The follow up question to, "Has TNG aged well?" should really be, "How much does a show aging well matter to you?" I think some elements date the show, but that's also, to me, part of the charm.
The early scores for TNG episodes are delightful--the catchy synth beats in "Booby Trap," for instance, are so awesomely 1989 I can't help but bob my head and turn up the volume to annoy my partner.

The slight corniness of TNG is one of the major reasons why I am so enraptured with it. So, objectively, I'm not really one to talk about TNG "aging well," now that I really think about it.
Do we mean "aging well" to mean that we could show TNG to some kid out of context without having to be like, "Now, son, this show is quite old and silly," and they would be like, "This is awesome, even for the current chronological age that I currently exist in! I'm a Trekkie now!" If we mean by those standards, I would say many aspects of the show's aesthetics have decidedly not aged well. But does it really matter? Don't the show's aged aspects constitute part of why TNG is so great?