On Bali island itself, the closest decent diving in my limited experience is Amed, which is a full 100km from the Conrad, roughly 2.5 maybe even 3hrs drive. My wife and I did one trip to Amed (a 5 night stay in Amed itself, maybe 3-4 days of diving), and that was just before Covid in Dec 2019. Did it with 2 Fish Divers a Padi 5-star IDC at the time (don't know if they survived), competent and friendly enough then, with a fair number of European (Francophones) dive professionals doing various certifications at the time. Vis was decent, currents not particularly strong, not difficult diving even though my wife and I hadn't dived in nearly 10 years at that time but the pool refresher brought it all back easy, like riding a bike.

Beyond Bali. you're probably looking at Pulau Penida/Nusa Lembongan, which is visible from Nusa Dua. But I don't know how you'd get there from Bali.