I agree with the recommendations to avoid the South east of Bali- the Kuta/Seminyak area- which is generally pretty awful, polluted, crowded, and full of drunken bogan Australians behaving badly.
Ubud is nicer, however still fairly crowded. The best time I had in Bali was hiring a scooter and getting lost out in the hills for the day- I eventually found 2 schoolgirls on a scooter who offered to lead me back to Ubud as the sun set, but man were they crazy fast! Beware of the road conditions! Good fun though.
Lombok was far less touristy than Bali and was great for cruising on scooters through monkey-filled forests, but your schedule probably would t permit getting over there and back.