Ubud is the best place to come for Balinese culture - the temples are beautiful and it's definitely worth seeing a show.  There are some lovely walks through padi fields and past artists houses and one of them most popular visits is the Monkey Forest and the Temple of the Dead.  The monkeys are relatively friendly but very demanding of food and if if you intend to enter the temple make sure that you are dressed appropriately.

There is also an extremely good market but you should be aiming to pay around a third of the price you are originally offered.

And when you intend to move on there is a range of buses to various places leaving in an ad hoc fashion throughout the day.

Recommended.

The island's other major destination is the cultural centre of Ubud, a charming but relatively commercialised town, where traditional dances are staged every night of the week and the streets are full of arts-and-crafts galleries.

It's a relatively short bus journey from Kuta and a great place to relax.  There is a huge selection of places to stay which vary wildly in cost.  Wealthy German and American tourists push up the prices in some places but you can still find decent accommodation (including breakfast) for around £5 ($8).  Some of the restaurants are expensive by Indonesian standards but the quality of food and service puts many western restaurants to shame - try the Balinese duck (which has to be ordered 24 hours in advance at a cost of around $10!).

Batur

One of the most popular destinations is the caldera containing Gunung Batur and its crescent shaped crater lake.  An incredible site as the bus reaches the edge of the caldera and you look down at the lake, villages and fields carefully wrapped around the imposing slopes of the volcano.

You'll have to get a lift down into the caldera but there will be plenty of jeeps waiting to take you to a mate's guesthouse.  Once you're there they will very quickly attempt to sell you outrageously expensive treks up the volcano (we're talking $50 for four hours work - the cost should be closer to $5).  If you don't accept there is a risk that they could turn unpleasant and if you attempt the climb on your own you could very easily meet an aggressive collection of locals.  Check where you intend to stay beforehand, ask around, and by all means try the climb (it's pretty easy and you can't get lost) but be very careful if you get into an argument with anyone - they have no rights but they do have knives.  It's a shame as it is a wonderful place and the cynical attitude of the locals is completely at odds with the vast majority of Balinese.