1) How much it cost if take taxi from airport to hotel
2) if take subway from airport to hotel, is it easy
Don't know about the taxi cost but taking the train is quite easy. The airport train terminal is at the domestic terminal. So if you are arriving at the international terminal, take the free shuttle to domestic terminal first. The airport train (kuko line) is vey frequent (7 min during peak hours). You will be boarding on stop K13. Get off at Gion station K10. The closest exit is exit 3 but if you want an elevator, use exit 6.
Finally, there are two Dormy Inn in Fukuoka, I assume you are going to this one.
The subway station is within 5 min walking distance from Hotel and it is very convenient to take subway from Gion station to airport.
Get an answer from Dormy Inn Hakata Gion staff and past guests.