Central Ubud can be covered on foot, but you will need some form of transport to explore the extended vicinity.
Ubud is generally a little quieter, and the streets calmer than the more urbanised parts of Bali. So whilst traffic is slower than in downtown Kuta for example, the sidewalks are often blocked by motorbikes, or a collapsed section necessitates a step off the sidewalk potentially placing you in the path of traffic. That traffic could be a tricycle or a truck, so keep your wits about you.
The EPL Phenomenon
Blame Elizabeth Gilbert. Those of you who managed to make it through the turgid best-selling novel Eat, Pray, Love, might have an inkling of what is coming up. Ubud features quite heavily in our heroine's search for fulfilment, and the knock-on effect in the town has been huge. Acolytes have swarmed to Ubud looking for and sometimes finding places and people referenced in the book. The actual characters mentioned are surely sick and tired of rather desperate looking thirty-something single women turning up on their doorsteps. The economic benefits of the novel to the area ratcheted up a whole other notch in mid-2009, when the eponymously named movie was shot in and around Ubud, Julia Roberts and all. Just be aware though that Ubud cannot necessarily guarantee a remedy for every mid-life crisis.
By road
As elsewhere in Bali, motorbike rental is widely available, and you will not be short of options. Expect to pay between Rp 40,000 and 80,000 per day for a late model motorbike in good condition. Look for rental agencies on all the main streets, or ask your hotel to organise for you. Navigation can be confusing, as signage is limited and all the roads look pretty much the same at first, but take it easy and stop to ask for directions if when you get lost.
By Local Car
Most local transport comes in the form of SUVs or minivans that can be hired with a driver for specific trips. Look for the circular yellow "E" logo on the windshield certifying them as Ubud Transport Association members. You can and should haggle a bit over the price, and pay less than for the equivalent journey in a metered taxi. A short trip should be less than Rp 20,000, and drivers will be glad to wait for you for a return fare.
Also, there are guys on motorbikes who will also offer bike rides ojek and are about half the price of those in a car.
By taxi
No metered taxis operate in Ubud, and any you see will be dropping off passengers from further afield.
By bike
You can rent bicycles for about Rp 20,000-30,000 per day. There is a large selection available at the corner of the football field on Jl Monkey Forest. Beware though: Ubud is very hilly, so cycling can be hard, sweaty work. Traffic on the main roads is heavy and drivers rarely pay heed to cyclists.
By Bemo
Bemos ply the main routes in and around Ubud, and the main stop and gathering point is Ubud market at the junction of Jl Monkey Forest and Jl Raya Ubud. Most bemos stop running in the late afternoon, and are always more frequent in the morning.
By Hotel Car
Many hotels are located out of town, and are happy to offer regular, complimentary drop-off and pick-up services to central Ubud. Expect to pay higher than taxi prices if you are intending to go further afield.