The Intercontinental at Jimbaran will be a good base location wise in the South, as it is somewhere in the middle of different things, but is also a great place to relax as a hotel and beach, so it will be a good use of time and experience even when you stay in. The south in general has a bit of a traffic jam issue all over, but you have to work with it. You could hire a driver for most days (about $30-40/day), and explore from there. There will be more stuff in the south to do, so I suggest 5 days there and 3 days in Ubud.
In my first trip I did almost everything in Ubud in one day trip from the South.