Can do if you know how to hunt cheap flights and decent hotels.
My partner and I visited Fukuoka Kyushu during Autumn November.
Mainly for hiking, onsen and attractions.
Here below is my cost for references only.

-----------------------------------------------

Fukuoka November Trip (12 Days):

- Philippine Airlines (RM2,590.22)

Hotels & Onsen Ryokan: (Total RM3,783.74)
- 1n x Toyohotel RM178.90
- 3n x Fico Hiji RM760.06
- 1n x Etavia Yufuin RM929.64
- 1n x Toranoyu RM611.09
- 5n x Toyoko Inn Tenjin RM1304.05

Transportations:
- 6 Days Car Rental (RM1108.74)
- Petrol (RM130)
- ETC Toll (RM150)
- Parking (RM80)
- Subway Fare (RM240)
- KLIA Transport (RM135)
- JPJ International Lesen (RM150)

Food, Snacks, Junks, Souvenirs & Misc: (RM3,000)

Shopping:
Nike Shoes x 3: (RM380)
The NorthFace Jacket x 1: (RM300)

Others:
Travel Insurances (RM105.75)
2 Pcs x eSim Data (RM56)

Total For 2 Person : RM12,209.45

-----------------------------------------------

Bonus:
Visited 9 Days Tokyo last May24 too with 2 Adults + 2 Teens.
Total Price 15K+ for 4 Pax (All in inclusived of Teamlab Borderless & Making Of Harry Potter tickets)