Definitely agree on the fact that Nusa Dua is purely touristic.

Wouldn't advise staying there.

Uluwatu is a must see and is quite beautiful, so is Ubud (2 nights max in my opinion, after, you'll get bored). Seminyak is the best place to eat well but there is a high chance you won't be able to swim since the waves are often 10 ft high.

Sanur is worthless

Do take a boat to the Gili Islands and/or Lombok, it's worth it

Favorite hotels: Legian, Four Seasons at Sayan and The Chedi Club at Tanah Gajah