Zanzibar in particular is a fantastic and exotic hangout with some of the best beaches in the Indian Ocean. It’s surprisingly un-crowded (sometimes nearly vacant) and can be a good value if you don’t spend too much on drinks. Bwejuu village in Zanzibar is the place to go for relaxation and hanging out on the beach in a very chill setting. Nungwi and Kendwa are known as the big party beaches.
Zanzibar is more developed than most of East Africa, so getting here is not difficult. I strongly recommend flying directly into Zanzibar as the ferries serving the island have been known to sink frequently. I flew Precision Air from Dar es Salaam to Zanzibar and found them to be good, although the ticket prices are higher than they should be.