How do I go up to Kagamiyama?

I will visit Kyushu in May. I planned to take a train from Hakata station to Niji no matsubara station and go up to the view point on Kagamiyama. From the train station, can I travel by a bus to the top of the mountain? If so, where can I find a bus station and where to get off? Please provide some suggestions.It would be great if you also show the bus schedule. Thank you.

http://www.showa-bus.jp/jikokuhyou_pdf/karatu_2.pdf

On the above bus schedule scroll down to the third timetable 七山線.
虹の松原駅前 is Niji no matsubara station
鏡山入口 is entry to Kagamiyama

Going up to Kagamiyama is a motorcyclist's dream with over 2 dozen hairpin turns - I've done it a few times myself - but there is no way a bus is going up that mountain.
Renting a car is the only real sensible way to the top.

What if I take a taxi? How much will it cost me?

If you are not going all the way to the top of the mt and only after the observatory site in Kagamiyama for the view of Niji-no-Matsubara, the 17 min taxi ride from Niji no matsubara Station is about 1360 yen. The ride from the Kagamiyama bus stop I mentioned on my first post is shorter, about 13 min but there may not be a taxi at the bus stop and the taxi fare saving is only about 200 yen (not to mention you still have to pay for the bus ride) so you might just as well take a taxi directly from the rail station.
http://www.nihon-kotsu.co.jp/taxi/fare/simulation.html?s=true&e=UTF-8&...

BTW, be sure to choose a day with clear sky for an unobstructed view. There was drizzle when we were up there and we had to wait a while for the clouds to disperse.

Thankyou very much for your suggestive information.

Yes my destination is the Kagamiyama observatory. I didn't plan to go further than that. And yes I think I will take a taxi. This might be the best option for me because the bus schedule does not match my arrival at Nijinomatsubara station.

If you find yourself having communication problem with the taxi driver, write down the Kagamiyama Observatory name of 鏡山西展望台 and show it to him. Or print out the webpage below for him to have a look highlighting the 西展望台 photo.

http://www.yado.co.jp/hana/saga/kagamiyama/kagamiyama.htm

I really appreciate your help.

Last question. I think I will need at least an hour to explore around the observatory. I will possibly leave at 5pm, and I'm afraid there might be only few taxis available up there by that time of the day, maybe none. What if I walk down?

Write down your intended time of leaving the place and see whether the taxi agree to come and pick you up again. We did it once when we took a taxi from Shimogo rail station to Ouchijyuku and the driver came and picked us up again after a couple of hours and no surcharge was added - couldn't say for sure in your case as the distance is longer. If you choose to walk it would take about 40 min.

https://goo.gl/maps/TYGmp

Thank you. I'm really grateful.