Am a huge fan of Indonesia. Greatest trip I ever did was slapping together something on easySABRE out of Jakarta with air and boat hops, pre-LCC. Last seat on a Sempati flight that stopped at Bali, Balikpapan, Ujung Padang and finally Ambon. Three days there and then the PELNI boat (NOT a cruise ship) with short stops in Manokwari and Biak and finally Jayapura (charming sorta city, BTW). Then the wait for a cargo plane into the Baliem Valley, three unforgettable days there, and Merpati back to Ambon by 2 stops just in time to catch PELNI to Bandaneira and the other great destination (center of the old nutmeg trade, lots of ruined forts, old cannon barrels just lying by the streets). Three days there and Merpati back to Bali, for another 4 or so before flying Royal Brunei to BKK via BSB. Total time including Jakarta was 4 weeks.

The Baliem and the Bandas were both totally unforgettable, though neither had so much as an ATM and very few restaurants. By today's rational standards the whole thing seemed a bit crazy, as I had only the flight framework pre-booked. English speaking also really drops off a cliff east of Lombok.

Today you can do weird moves like fly back to SIN or KUL to get someplace else in Indonesia, as it's probably cheaper that way. I was inspired by being a bit bored in Jakarta and reading ahead in the Lonely Planet Indonesia tome. Was lucky NOT to have someone around to talk me out of it, as it was a bit seat-of-the-pants and some areas would later become unsafe.

Your plan is very do-able, though you get to share the places with a lot of people. I liked Yogya and there's even a scenic Indian Ocean beach not too far away (can get chilly and windy, though), and of course you've got sites like Borobudur, Pranamban and the Dieng Plateau. Bali can be done very cheaply but all the hawkers trying to eke out a living in Kuta, Sanur and Besakih can be annoying (Nusa Dua basically fences 'em out). Would bet on Bali for the culture and Lobok or the Gilis for the beaches.