I would suggest you start in Java. Have one night in Jakarta (it's like any other city - there's nothing special to see), then get a day time train to Yogyakarta and do a day trip to Borobudur and Pramamban temples - spectacular at sunrise. Yogya is good for 2 or 3 nights.
You can then go to Mount Bromo which will be a day's travelling (and I mean a full day) then getting up at 3am for the sunrise over the famous 3 volcanoes. Straight after you can then get transport to Bali by bus and ferry (remember Bali is one hour ahead of Java).
Gilli islands are highly recommended for the beach, clear waters and diving. Bali, has ok beaches but Kuta is a nightmare place - best to stay away and try a quieter beach like Sanur or Padangbai (incidently this is where you can get the ferry to Lombok so you can get to the Gillis).
We really like Gili Trawangan, lots of nice beach bars and restaurants and lots of good quality accommodation with different price ranges. Excellent and cheap food and drink. The diving is good, even the snorkelling is great just off shore with turtles, clown fish, parrot fish and angel fish amongst just a few to be seen.
The best thing about this route (we did this last December) is that you can do it all overland reasonably cheaply and you see so much more of the country than flying. Java was definitely a highlight of our - so far 2 years - of travelling and we could spend weeks on the Gillis just relaxing and chilling out.
Hope this helps