Kuta is near the airport, and most hotels offer free airport pickup. If hiring a cab, go to the airport's official taxi counter, where you'll pay a set fare, typically Rp60,000.
Kuta is a big rectangle. The two main north-south streets are Jalan Pantai Kuta and Jalan Legian. They're connected east-west by Jalan Benesari, Poppies Gang I, and many quaint gangs (alleys). You can easily meander in and out of these small alleys and do some window-shopping or take the reasonably priced blue-and-yellow metered taxis. The horse and buggies (cidomos) are ridiculously overpriced: From Pantai Kuta near Hard Rock Hotel to Jalan Double Six (about 6km/3 3/4 miles), the cost is Rp150,000 -- equivalent to an average local weekly salary!
Taxis are available everywhere in Kuta, but be sure to ask them to put on the meter. Most taxi companies are reputable, such as Blue Bird and Komotra taxis, but beware of the white taxis who often try to scam naive tourists.
Recent street name changes in Kuta include: Jaalan Pura Bagus Taruna is now Jalan Werkudara; Jalan Segara is now Jalan Jenggala; Jalan Kartika Plaza is now Jalan Dewi Sartika; Poppies Gang II is now Jalan Batu Bolong; Jalan Stria is now Jalan Kediri; Jalan Pantai Kuta is now Jalan Pantai Banjar Pande Mas; Jalan Padma is now Jalan Yudistra. Locals, business owners, and maps will use a combination of these names.