Best Travel Destinations in Indonesia

 http://www.quora.com/Indonesia/What-is-the-best-travel-destination-in-Indonesia

For places of culture and heritage, there are plenty of choices, however I think the most popular ones would be Toraja, Yogyakarta, Solo, and Ubud. For great beaches, Bali, Gili and Belitung islands are still among the best. 
For diving experiences, I would choose Derawan, Pulau Komodo area (Labuan Bajo, etc), Raja Ampat, Gili. For laid back shopping and hanging out, Bandung is the way to go
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I was in Indonesia in August 2010 and thought everywhere I went was beautiful. Kuta in Bali is OK if you want to party all day and all night - quite a young atmosphere with most visitors in their late teens or early 20s.

Singeggi in Lombok is beautiful, far less tourists although it is quite difficult to sunbathe without constantly being asked to buy something - I found the nicest way to pass the day was to buy something, make friends and learn something culturally new! Found it to be fairly couple-y though, not somewhere I would travel to at that time of year alone. Kuta, in the south of Lombok boasts some of the nicest beaches I have ever seen, a great spot for surfing.

My favourite place was Gili Trawangan, 24 hour party place but also gorgeous beaches. I stayed 10 days and could have easily stayed a month! It was difficult to find decent affordable accomodation at peak season though.

And finally, Mount Bromo (on Java) is an absolute delight to see, an early morning start to be driven to watch the sun rise over the volcano! Dress warmly though as I was in shorts and t-shirt when lead to me having to rent a very thick jumper and buy a wooly hat from the head of an Indonesian tour guide to wrap around my feet!
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- Sumatra is definitely a place to see. Food there is amazing. Masakan Minangkabau is probably my favourite.

- I also agree with Patricia. Lombok is a better experience than Bali. Climbing the gunung Rinjani is a tough but rewarding experience... and the gilis are a wonderful place to chill out.

- Solo & Yogjakarta are very cool place and Borubudur is a unique place to visit... to me Borubudur is as amazing as Angkor Vat.

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Try to visit Bandung, place named "Braga",
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Lake Toba and Tuk Tuk Island in North Sumatra
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K-shaped Island of Sulawesi is really special. It has the second greatest biodiversity in the world after Madagascar. Even Sumatra can't match that!
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you can explore one by one, for example the West Java you can start in Sukabumi Ujung Genteng, Serang Sawarna Beach and Kampung Baduy, after that you can go to Garut to see Kampung Sampireun, Kawah Papandayan and the other good places with different unique
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for diving you must visit this place...... Raja Ampat (Papua) the best spot diving, Takabonerate (South Celebes) the 3rd largest park  coral reef in the world, Bhunaken (North Celebes) it's beutiful place.....
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Putri Island near to Jakarta is great. A small island, peace and silent...
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in East Java, there are many hidden places, virgin places such as Tanjung Papuma Beach in Jember
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Ramadhi Irawan, Clueless traveller

My top 5 travel destination in Indonesia are (in no particular order)

1. Derawan Island (Image search: derawan island)

Derawan is located to the east of Borneo (Kalimantan). It is a group of small islands.

I like this place for its beautiful beaches and its unspoiled nature. Not many travellers visit this place due to its remoteness. You will have to switch between plane, ships, cars multiple time to reach here. But once you are there it is worth it  Location: Google Maps

2. Mount Bromo

Mount Bromo is a vulcanic mountain located on eastern part of java (close to Surabaya).

This is one of the most popular destination for travelers (local and foreigners alike). Mount Bromo is an active Volcano, and the last eruption was in 2011. This is not the highest mountain in Indonesia, but often considered as the "must-visit" destination for hikers.

I like Mount Bromo for its view specially to watch sunrise at the peak of the mountain. It feels as if you are above the sky (Sunrise Bromo - Google Image).

3. Mount Kelimutu

I particularly like this one because its uniqueness. The mountain has a lake/crater of varying color (Danau kelimutu - Google Image Search). Located in Flores (about 650km east of Denpasar, Bali) is still do able, some airlines and ferry does have route to the Flores island where the Mount Kelimutu is located.

If you go here you might as well stop by at Komodo Island (Dragon Island) where you can see Komodo Dragon (Largest lizard on earth) and do some snorkeling / diving in the region of Labuan Bajo where you can spot unique fish such as Manta Ray, Hammerhead Shark as you can see below

4. Bali Island

I just like this place because its vibrant environment. You can enjoy beach party, got to pub/bar have a drink, do crazy things you won't forget for your entire life. There are some great surfing spot as well.
Well i am sure you have heard of this place.

5. Raja Ampat

By far, this is one of the most beautiful, most remote and most expensive travel destination of them all. Situated in the Papua Island (Locally known as Irian Jaya) it has a reputation of being one of the best diving spot on earth.

It has diverse fish species and beautiful coral reef, crystal clear water and unspoiled and calming nature is difficult to compare with.

Unfortunately travelling here will cost you an arm and a leg. First of all it will cost you around 1500 EUR to 3000 EUR for accommodation only (usually this cost includes meals, diving, snorkeling). Second of all Raja Ampat is very remote. It is utterly far from big city. First you need to go to Sorong the closest city with Airstrip, then from there you need to continue your journey by Boat to Raja Ampat