Best train tickets for Hakata-Togo?

I will be staying in Fukuoka, (Munakata) Togo for a month with family. On most days we are likely to stay in Togo area, but on some days we want to go to Hakata and possibly other nearby locations. I noticed there are a number of local discount tickets, but it was not easy to determine if any of them would suit my purposes.
A one way trip between Togo and Hakata costs 560yen. Is there some discount ticket that would make sense, or should I stick to individual tickets?

IC card would problably be best for just commuting around leisurely.

There are other pass for only Fukuoka area or northern Kyushu. Both on the JR kyushu website. But you would save up those and travel in daily clumps ro make then pay off.