Ubud is pure relaxation, enjoy the calm atmosphere, Visit the "Monkey forrest" but don't bring food even though people are trying to sell you bananas on your way into the forest - or you'll run the risk of being attacked by the monkeys.
Go to one of the towns dancing theatres which perform the beautiful sagas Ramayana and Mahabharata, which the town is so well known for. It lasts 1 to 3 hours, but it's worth it-- their outfits and masks are very beautiful.
Quick Tips:
Go to Cafe Wayan for a wonderful meal -- even though it's a bit expensive, it's worth it.
Rent a motorbike a go for a drive around the beautiful rice terraces in the area surrounding Ubud.
Best Way To Get Around:
If your not up to driving yourself - you can rent a car and a driver for about 25 for half a day, and see some of the areas attractions.
The Shuttlebus is another VERY inexpensive way to travel around Bali. The trip is usually not a pleasant ride - very bad roads and busses without shock absorbers, but it is quite an experience and adventure. You never know if you have to sit on the floor or sit on your travel partners lap, because too many have been booked on the bus. A trip from Ubud to Lovina cost about 2-3 - and the view is great - unless you sit on the floor.
If you suffer from motion sickness - take a pill before going.