I'd recommend Yogyakarta if you're on Java. Loved it there. Touristy but not overly so. Plenty to do and see in the way of arts, crafts, culture and places of interest. Did a day visit to Prambanan and Borobudur (mentioned by Don). Did it the wrong way around to catch the sunset as Borobodur closed, but well worth a visit to both. Yogyakarta itself is great Lively, friendly, relaxed. Nice contrast to Bali where was a bit more manic and busy.
Also had a couple of nice relaxing days on Nusa Lembongan an hour or so by ferry from Bali. We didn't do much other than chill but I think it's a bit of a hotspot for diving, snorkelling and the like.
Spent a couple of days in Labuan Bajo so we could visit Komodo Island. That was good - day trip included visits to other islands and a stop off at Manta Point in the middle of the sea so people could go snorkelling amongst the manta rays.
I didn't see much of wider Bali, but if you're concerned that it's overly touristy you could perhaps consider a few days visiting another area to escape from it and experience something a bit different.