Generally Japan is thought as been culinary mecca but with the exclusive taste comes a large exotic price tag.
However there are many delicious options that won't blow your budget. All you have to do is open your eyes and follow your nose.
Hakata is famous for its Yatai(food stall) and pork soup (ramen). However a lesser known equally delicious and motto healthy option are the restaurants that specialize in Tori.
One place in Nagahama (30mins walk from Hana Hostel) has a very delicious and cheap Jidoori (aged chicken) The restaurant offer you "All you can eat JPY 1300 /person" . It freshness is something I have never encountered before and the JPY 100 beers make it the ultimate weekly stop for this Kyushu native!
I can take you there if you want :)
Have a great weekend :D