Now how about suggestions ranging over the rest of the island for a further 2 weeks? We want to get the most out of it by doing and seeing as much as possible.
I would strongly suggest you go to Ubud and have a look around there. Find Nuri's and annoy Roy

and then head over the hill to Lovina. Once there do the tourist tour and look at all the sights. From there head on back south via the coast, west or east is up to you.
Do not discount Kuta and environs totally as it will show you the tourist side of Bali and that maybe what you want or it may make you appreciate the Balinese side of Bal most. The easiest way is to get your self a car with guide as it is too short a time to see more than a glimpse. Even take a visit to Denpasar.
After that you can start thinking about really getting to know Bali and the Balinese and for that you really need to ask Roy, Sanurian, Richard Kalibukbuk. You can then book your long term stay out of the tourist environs as that is the only way to get to know the island and its people.
Have a good time. I will be there in the airport from midnight on the 24th until I catch my flight onwards the next day at 9 am. Anybody who wants a free drink and to keep me company is welcome.