The difficulty with Japan is that it's not really geared up for budget travel, so you have to find creative solutions sometimes in order not to spend too much money.
Food: If you can get into the habit of buying picnic ingredients from supermarkets (fruit, bread, sandwich fillings etc.) and eating a hot meal a day from a cheap restaurant that will set you back (in total) perhaps AUS$28-40 per day. (You might spend a bit less, but it's safer to overbudget). Bear in mind that alcohol from supermarkets is not too expensive but in bars it's tremendously expensive (AUS$11 for a half litre of beer!).
Supermarket sliced bread is a little more expensive than you might expect, but then the Japanese are accustomed to snacking on small dishes of rice (which, unless you come prepared, are a little difficult to cook while travelling), rather than sandwiches.
Bear in mind that supermarkets and local groceries are sometimes difficult to find (especially when you've just arrived in a new town) because they are heavily outnumbered by the 24 hr convenience stores such as Lawson, Family Mart and 7-Eleven. The convenience stores offer pre-packed, processed food and are predictably more expensive than shops where you can buy food in a slightly less processed state.
Accommodation: This is where things get really difficult. There are no budget hotels in Japan and no hostels as such. (There are 1930s-style youth hostels, but they are for youth groups, have curfews, lights out, no drinking etc.). This leaves you looking at (in order of most expensive to least expensive): luxury hotels, traditional Japanese inns (ryokan), business hotels, traditional Japanese B&B (minshuku), love hotels, capsule hotels, your tent.
A night in a business hotel will set you back about AUS$85, a night in a minshuku or a love hotel perhaps AUS$70. Minshukus are family run and like you to ring up in advance of your arrival. Some don't take foreigners. Capsule hotels (AUS$64 per night) can only be found in the port cities (Yokohama, Tokyo, Osaka, Hiroshima etc.) and generally don't allow girls.
I'm still not sure what the rules are about camping in open coutnryside in Japan, but after various accommodation options had practically bankrupted me every time I went travelling across Japan when I was living in Niigata, I opted to buy a tent with a Canadian colleague and we travelled for a week in Shikoku, using the tent as our accommodation. This was successful, but it only worked because John had a car and we used to slip out of town after dark, find a quiet place beyond the suburbs to set up a tent and sleep until dawn.
I wouldn't recommend camping on your own (not because Japan is particularly dangerous, I just wouldn't recommend it anywhere), so you might also need a friend to make this option viable.
Spending money: Think about what you spend on a weekly basis at home. Double it. (Again, this may be overbudgeting, but better that than being caught out).
I think you're looking at a bare minimum of AUS$100 a day (and a little more if you want to be comfortable). Over 3 months that would come to AUS$9000.
If this seems way out of reach, the best option might be to find barwork or part-time teaching work and then travel in your time off... then at least you will be earning while you're spending.
Another way to save on accommodation (definitely the biggest cost) might be to join a network where travellers allow you to stay in their home as their guest for free in exchange for your allowing other travellers to stay in your home as your guest in Australia. I'm going to do a bit of research and see if I can find anything along these lines on the web for you.
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I am looking at spending around 3 months (or longer) in Japan. I want to check the whole country out but have no idea on how much money I am going to need to cover food, accommodation, spending money etc. Don't need anything flash to stay in just the basics will do. Any rough estimates?