"Data's Day" is actually a pretty great one to get someone into TNG, it's fun, but most importantly, Data is essentially walking around introducing all of the main characters to the audience.
I typically recommend starting with TNG in general (I used to say because it was "modern" π) as it naturally leads into DS9 and VOY. That said if your friend doesn't typically watch older shows but is open to them, then just starting with SNW or ENT is an excellent intro to the rest of Trek.
Happy to help! I would love it if you report back, we used to get 100 "How do I get a friend into Trek" posts/day on /r/StarTrek but very few follow ups on if it stuck!