We spent a total of 45 days in Indonesia, traveling with a low-mid range budget, meaning that we slept mostly in private budget rooms and ate two meals out every day, alternating between a restaurant and cantine/street food. The total amount spent was $4,793.96, with an average of $106.53 per day and per couple.
Below is a breakdown of all the expenses in Australian Dollars (AUD) for the two of us (conversion rate AUD to IDR at that time was 1:10.400):

Transport
This was our biggest expense. We got in the country flying from Kuala Lumpur to Medan, Sumatra, which was an inexpensive flight ($80 pp). We took a few domestic flights, and some of them were quite expensive. However, it was the most suitable option for us for changing islands quickly and avoiding all the hustle.
Also note, that we had to do a border run to renew our Visa because we did not get ours prior arrival. The border run consisted of 3 flights Yogyakarta – Jakarta, Jakarta – Singapore, Singapore – Surabaya. That added $330 to our expenses. However, that saved us around $70 pp (for the Visa in advance plus the extension). In addition, it saved us 3 visits to an embassy to do all the paperwork.

On top of the local flights, we spent $180 on our entry ticket to Medan from Kuala Lumpur. Another $280 that we spent mostly on public buses or taxi. Every so often, we would also take a Grab, which is very recommendable for tourists, as taxis and local buses will most of the times try to rip you off at the exits of train/bus stations or Airports.
Activities
This was our second biggest expense, and honestly, it was a bit unexpected. The fees in some places are can be overpriced from our point of view.

Additionally, in some places, they have different fees for locals which could be a third of the tourist fare.
Accommodation
Accommodation price in Indonesia is very fair. We would mostly sleep in a private double room, in guests houses, where they would provide a simple breakfast the next morning. It was also a great way to meeting other fellow travelers.
Overall, $17 dollars per couple on average ($8.5 pp) is not bad at all, considering that most of the nights we had our own room with toilet and shower. It is fair to add, that in many places we didn’t have warm water. However, who needs a hot shower in the tropic.
Food
Averaging $18.36 per day. That is eating twice or three times every day outside. A good meal in a nice restaurant in Yogja for two people would be $10, whereas eating in a cantine or in a street food market would cost $3 for both of us.
Alcohol
Alcohol is expensive in Indonesia. We would mostly drink beer every now and then and we would pay $3 to $4 for a 650mL bottle in most of places. It is usually Bintang. They do not have much variety.
Miscellaneous
This category is for things like laundry, toothpaste, deodorant, sunscreen, mosquito repellent, new headphones, haircut, souvenirs, sim card and internet, non alcoholic drinks and other snacks.
Withdrawing Money
In Indonesia, you need to carry cash with you all the time. Most of our transactions were in cash and we had to plan ahead for ATMs, as in remote areas it is difficult to find any. Before leaving Australia, we signed up for Citibank plus. This allowed us to avoid withdrawal and exchange rate fees. We would only pay for the exchange rate that the local bank would apply to the currency. After trial and error, we eventually found that Mandiri bank would apply the best exchange rate, which was only 1% more than the google conversion.
This trip cost us $1000 more than what we had budgeted as we did not expect some of the expenses (flights and some of the entrance fees). However, Indonesia is still a very cheap country in terms of accommodation and food. And even though transportation can be expensive, one can always take public transport, if time is not a problem and there is energy to spare.