Nowhere that I know of close to Nusa Dua that is particularly good. Geger Beach in Nusa Dua is worth a visit. It's a nice sandy beach and you can buy simple meals and drinks there. If you turn right as you reach the beach and walk towards the rocky headland, there is some reef with low key snorkeling.
Blue Lagoon at Padang Bai is quite good, but you need to be there before the waves get up a bit and it's a fair way from Nusa Dua. Right in front of the Vienna Beach Hotel in Lipah village [that whole area is known colloquially as Amed] there is an extensive coral reef with lots of fish. But Lipah is further on from Padang Bai. The best time there is at the least rise and fall of the tide.
We generally stay for several days in the Amed/Candi Dasa area and that puts us close to the snorkeling. Hiring a driver and car is very reasonable in Bali, about 300,000 for a long day, including petrol. Don't let your hotel arrange it for you as that is likely to cost you more. Even if you just go for the ride, it's worth seeing Klungkung for the heritage buildings. Padang Bai, the ferry port for Lombok, which is like an old Balinese fishing village apart from the ferry terminal. Candi Dasa, not everyone's choice, but one of my favourite places. And Amed, with the scenic, undulating coast road from the south and the beautiful mountain/valley scenery and rice terraces on the inland road on the way back to Candi Dasa.
You can also go on a cruise out to the island of Nusa Lembongan and this can include snorkeling.
You can hire snorkeling gear, but I prefer to take my own.
Hope this info helps.
Just another word on getting ballroom dancing shoes. The soles don't look like your English ones, but they brush up OK. They're not as light or as flexible as the English ones either, but at about 1/7th the price of my English shoes bought in Australia, they're quite good value.
We've never found much dancing [as we know it] in Bali. There was supposed to be a tango club [probably Argentine] in Seminyak, but I've heard that it's not there now. You can get up and jive and do rumba and cha cha in some of the restaurants, probably on ceramic tiles. The musos are very versatile, give them a tune title and they can probably play it. The Peninsula Hotel has a nice wooden floor in their restaurant, maybe OK if they have music. If you get up and dance, you will probably find that others will be encouraged to join in.