If you don't feel like spending money but want something sweet (or otherwise) in Hakata Station, I've got a recommendation. Actually this is ideal if you're shopping for omiyage, but even if not, if you have some time to spare, this is sort of fun.
On the North side of the first floor of Hakata Station, there are restaurants and tons of stands selling omiyage. You'll notice there are several locations with the same products, and often the same free samples. Not every area gives out samples, but most of the samples are large and sweet. Several savory samples and even samples of local alcohol exist as well, especially towards the back where you can try out dashi and of course the local specialty, mentaiko. These are mostly the same exact stores that are everywhere in the region, selling just about the same products, but most of the bigger stores don't give samples.
Another local specialty is "menbei," or mentaiko flavored senbei.
It might be tough to avoid spending money or getting yourself into a sugar coma. I recommend trying only the things you know or think you like, and when you feel yourself hitting saturation, head for the nearby Kaldi Coffee Farm for a sample of coffee. Better yet, to start off get a nice hot black coffee to go and carry it with you to cut the sweetness of the samples. Don't take samples of the same product more than once, even if you see it five times. There is plenty to get your blood sugar high enough without it.
This was my favorite sample - huge Hakata amaou strawberry flavored treats.
Most of the omiyage in Japan are beautiful and come in beautiful packaging. It's also fun to just look at all the pretty cakes and manjyu.
Depending on the season, there will probably be decorations. I saw a Santa recently and close to Valentine's day they had a pop up romance shrine where couples could leave messages written on heart shaped papers.
Have fun & if you're not in the area, I'm sure this type of omiyage parade exists in most larger cities.