Some advice to go around java-bali-lombok.
a good place in Jakarta, “monas” (national monument) the’ve museum about indonesia and also u can go to up the tower. next u can go to “kota tua” is like old town, also have museum but u have to go in the morning, u can rent old bicycle too for ride bikes. he beach is “ancol” the place is good but the beach is so dirty. u can play in “dufan” like disneyland, and go to sea world, not realy big aquarium, for many fish, turtle, and shark. next u can go to “taman mini” park, thats miniatur for indonesia, many culture around indonesia and from many island in indonesia, and also have imax theater.
place near jakarta is thousand island or in bahasa is pulau seribu. they’ve many island there and have a good underwater view, but the beach not so good in some place. Some good island is tidung island, harapan island (hopping island), pari island, and many more. And also anyer beach in west java.
next u can go to bogor, good place for looking beautiful view from the top, like summit but u can go to by car, they’ve tea tree, also small safari, zoo but go to by car inside the zoo.
Next go to bandung in west java, still about view and hangout place, for shoping too, good view there, and also ciwidey kawah putih (white crater) in bandung, is like a lake but the color is white. also they have beach in pangandaran. and good one is batu karas beach, u can go to “green canyon” river, they’ve cave and you can swimming in the river. For rafting in sukabumi.
if u go to next central java, u can go to semarang. they’ve big old building and little bit scary i think, is “lawang sewu” means thousand door, and also u can go to harbor in jepara (2-3 hours from semarang) and go to karimun jawa island. that a good island with white sand too.
and after that u can go to yogyakarta and solo, they’ve many temple. the big one is “borobudur” temple, for buddha religion temple near yogyakarta (in magelang), the last time borobudur include in 7 wonderful place in the world (old version), and the other 1 is Hindu temple “prambanan” temple. they’ve mountain too but not really good, and the way to go there is so long and scary. In Yogyakarta have shoping place too in malioboro street, good for ride bikes. And also can go to rafting in there. They’ve “kraton” too, is like a old kingdom in Java.
next u can go to Surabaya or malang in east java, u can go to sempu island. and also “bromo” mountain. thats a good place for trekking and make some adventour in the mountain. also big zoo in java if u want to see many animal from all world in “Jatim Park 2”.
next for bali, u can go to south bali for shoping and party in kuta and legian street and also in seminyak, kuta beach have cheap hostel in poppies area. u can go to “nusa dua” for water sport and diving, but the good one for beach and diving is in east bali like “amed” beach, or swimming with the dolphin in north bali “lovina” beach
for good place to stay with culture and village, u can go to “ubud” the’ve monkey forrest, and ricefield, also have traditional dance and good massage.
if u have more day, u can go to lombok island, next to bali. senggigi beach, they’ve good island to go, gili trawangan, gili meno, gili air. the big one is gili trawangan, no polution because they only have bicycle and “cidomo” is like horse-drawn carriage. in lombok again, u can go to for trekking in rinjani mountain, if u dont have time u can just go to the waterfall in there. also in south lombok like kute beach.
next u can go next to Lombok, flores, komodo island only one in the world island full of comodo, and also they’ve many virgin island, in flores and kupang.
for bali and lombok have many cheap hotel, so easy to find it. for dormitory is like 50.000 rupiah ($5-$6) for hostel from $10-$30 per night. but sometimes the cheap one dont have air conditioner. u can chose many hostel there. for hotel, the good one is from $30+
well, thats some advice from me, some of that place is the place i visited before. hope the advice is help u.