1 day pass from Hakata station to Dazaifu

Hi, i would like to find out what is the best way to travel from Hakata station to Dazaifu. I will be arriving in Fukuoka international airport. Planning to leave the luggage in the hotel (Hotel Tokyu Bizfort Hakata) which is nearby to hakata station. Since i had a night flight before, i was planning to take a quick rest and then just head to Dazaifu and Tenjin.
I'm checking out the hotel the next day to Oita and will only have 1 day to spend there. Is there a 1 day pass available for me to use ?

http://www.japan-guide.com/e/e4854.html
http://www.hyperdia.com/en/

Not need any pass
buy Hayakaken(IC card ticket) at FUK subway station.
http://www.emoneytouch.com/2009/04/30/1647.html
http://en.wikipedia.org/wiki/Hayakaken

There is the way to get on the direct bus in order for you to go to Dazaifu from Hakata. Travel time of it about 42 minutes, fare is 600 yen. It starts from stop No. 13 of Hakata bus terminal.
http://www.nishitetsu.jp/pdf/bus/201403_bus_hakata_dazaifu.pdf

I guess in order to go to Tenjin from Dazaifu, it is preferable to use the Nishitetsu line, and is economical.

The pass you're referring to is the Fukuoka Tourist City Pass:
http://yokanavi.com/access_tourist_eg

The most famous place in Dazaifu is the Tenmangu shrine, and Komyozenji Temple next to it, of course. Plus the National Museum. Aside from those places, there is not much of intense interest.
Fukuoka City has a number of good places though. You can get a good list of what to see and do on:
http://www.tinyurl.com/see-fukuoka

If you're going to Beppu the next day, there are some great places there as well. The Hells Tour is great and only takes a few hours to see at a leisurely pace:
https://www.youtube.com/watch?v=K2NNi8MLcXM

Plus the Monkey Park/Aquarium is nice as well:
https://www.youtube.com/watch?v=zepPfkuqhok
And if the weather is good, the view atop Mt. Tsurumi is terrific:
https://www.youtube.com/watch?v=cBnZneDsKqQ

Enough to keep you quite busy.