Worth to buy Fukuoka & Dazaifu City Pass

I'll travel to Dazaifu from Gion (Fukuoka) station, 2 way plus a few train rides within Hakata or Tenjin area. Is it worth getting this pass just for the train rides? Or best to pay as I ride using a Suica card?

Ultimately it depends on where you are going, and your total plans. It's only a 1-day pass, and you will have more than a day's worth of sights for both Dazaifu and Fukuoka City itself. The pass also gives a few slight discounts at some places, but they don't amount to that much. The one way fare to Dazaifu is just 420 yen and it just takes 35-40 minutes. Unless you are taking a whole lot of subway and bus trips, it doesn't look economical to me.
An alternative is to get a subway 1 or 2 day pass if going around the city (many good places aren't far from a station), and just pay for the round trip fare to Dazaifu and back. Dazaifu Tenmangu Shrine is the big draw there, and you can easily walk there from Dazaifu Station. To get to Dazaifu, it's best to go to Tenjin Station and take the Nishitetsu train there - if you can get a ltd express train (which doesn't cost anything higher), then so much the better. A local train that stops at every single station would waste a lot of time though. You'll need to change trains at Futsukaichi Stn.
Since you mention Gion, don't miss Tochoji nest to Gion Station - you can see Japan's largest wooden carved Great Buddha. Nanzoin just outside the city is well worth it too, plus Ohori Park, Maizuru Park with the castle ruins, and TeamLab Forest at the Paypay Dome.
https://goo.gl/X3LDaE