While most hotels don't yet have in-room internet availability, most have a business center or lobby area with internet access available. As with most things, access in the hotel is more expensive than elsewhere. As in the rest of Bali, there are plenty of shops offering internet access. These include stand-alone shops, "Wartel" shops that offer internet access as well as long distance telephone service, and cafés where you can get food as well internet access. Among the latter is ESC on Legian Street near the bomb site.
Expect to pay 1,000 Rupiah (0.06 USD) per five minute block for internet access at shops.