I agree with Mike Veitch (post # 5), maybe 3-5 days in the north Menjangen to Lovina, 3-4 days around Tulamben-Amed, and around 3-5 days diving from Padang Bai (you could stay in the Candidasa area, maybe better restaurants than in Padang Bai proper, not sure). You should plan on staying at all three places, and moving on once you are done with each area.
I would contact a few operations in Bali to see what they offer you - they all generally can easily put together a package for you, starting from airport pickup, accommodation to suit you, diving and all transfers. I've used Aquamarine Diving 3-4 times myself and can heartily recommend them, they are not the cheapest, but they provide an excellent experience, and will work with you to plan something suitable.
For land activities, Bali is a small enough island that I would do that after the diving is over, with the exception perhaps of the Menjangen area (north west), you may prefer to spend an extra "land" day there while you are there for diving. Watch out you don't get an overdose of temples - plenty of temples to see in Bali, that's for sure! Apart from the usual more famous attractions - the Botanical Garden was a pleasant surprise to me -very big and peaceful. The Butterfly Park was also neat.
How much diving do you want to do? Why not consider Lombok as well? (I haven't been there myself, just a suggestion since you have 3 weeks)
Have fun!