The southern tip of Bali is far and away the most developed area. While there is an almost unbroken string of resort districts stretching north of the airport, each of them has a distinct character, as described below. The "teardrop" south of the airport is a small hill, called the "Bukit" ('Hill' in Indonesian). The Bukit slopes up quickly, and is edged by cliffs on most of its western and southern sides.
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Kuta / Legian / Seminyak / Tuban
Stretching north of the airport on the western facing side of South Bali's long peninsula is a seemingly unending stretch of hotels, bars, restaurants and tourist shops. Tuban, just north of the airport, is the most recently developed of the areas, with some shopping centers and upmarket hotels.
Kuta is the oldest district and where you will find the highest concentration of hotels for all price ranges, as well as everything else. It's also the most congested.
Next is the slightly quieter Legian area. The Kuta-Legian beaches are some of the most popular with surfers, and the best places to find lessons for beginners, but they aren't the best for sun-bathing or other water sports.
Seminyak is the place to stay if you want to be well away from the crowds, but within a short taxi ride of shopping and nightlife. It's not nearly as developed. You'll even see a rice field here and there if you explore the district. I happen to think the beach here is much better than those further south.
Sanur
The main resort area on Bali's east coast is also the oldest one in all the island. Sanur has a reputation for attracting a more 'mature' crowd, and thus is thought of as a bit more quiet than the Kuta Legian area. In fact, some wags refer to it as "snore", but the area is becoming increasingly popular, with a wide range of fine restaurants. A wide, flat beach with a protecting reef makes Sanur a great place for windsurfing, snorkeling, etc. but not so good for surfing. Sanur appeals mostly to families and those seeking a more relaxed vacation.
Nusa Dua
On the eastern side of Bali's southernmost point is the exclusive resort area of Nusa Dua. This is where you'll find the very expensive five-star all-inclusive resorts such as Club Med and their imitators. The area is generally for those that want a tropical getaway without the hassles of dealing with a foreign culture.
Jimbaran
South of the airport on the Bukit's west coast is Jimbaran. Once a sleepy fishing village, Jimbaran is still famous for its many seafood restaurants, where your selection of fresh seafood is barbecued and served to you right on the beach. In recent years, the area has also become home to some of Bali's poshest resorts, such as the the award wining Ayana or the ultra-lux Bulgari Resort.