Yes, Catherine, I agree with TurboRook -- we hired a driver one day and he took us out to all these little "craft villages" around Ubud. Different villages had different specialites (puppets, masks, woodcarving, silver, batik, etc), and the prices were cheaper than in Ubud. Plus in some places you got a bit of a "workshop tour". The scenery was beautiful and it was a very nice day out.
Also - this was our "super touristy guilty pleasure" - we loved the day trip of rafting on the Ayung River followed by an elephant ride. Both were so-oo beautifully scenic! It's the only time I've ever ridden an elephant, and we went all around a village and through the countryside - fun! The Monkey Forest in Ubud is also great - bring lots of bananas! (Can you tell that we love animals but don't see many of them here in Manhattan?!)
We spent our time in Ubud and Jimbaran Bay, and no big party crowds were in evidence. (This was in August 2003, so tourism was still down in general). We boarded our Komodo liveaboard in Tulamben, which was pretty far out and very quiet.
Bali itself is not a hostile island, but it has been a target of bombings twice now, so of course there are no guarantees. The area around Tulamben is probably particularly low risk because it's just not a well-known tourist area. Good news for divers!
I felt safe on Bali, had a wonderful experience, and would return in a heartbeat. But, then again, I live four blocks from Ground Zero. And I don't have children. I'm sure both these things shape my perspective. No place is completely safe, so - for Bali or anywhere - all you can do is consider the known risks and make a decision based on your personal comfort level.