Kumamoto Question

Hi, I'm planning to visit three places in Kumamoto as a day trip from Hakata:

1) Suizenji Garden
2) Kumamoto Castle
3) Honmyoji Temple

However, I'm not sure which order I should visit, in terms of minimal or no backtracking. Individually, I know how to get to each, but can anyone recommend a route which I should take? I intend to start and end at the Hakata Station, starting from early morning (after 7am).

Also, if anyone can suggest where I can get some lunch along the way, it would be appreciated as well.

Thank you!!!

City tram covered all no problem.
http://www.manyou-kumamoto.jp/en/travel-tips/inner-city-transportation...
http://www.kotsu-kumamoto.jp/Content/media/pdf/routemapE.pdf

Oh great, the map is exactly what I needed. Thanks a lot!!!

Lunch: The second floor of Kumamoto Station has an array of restaurants. There are also many around Suizenji Jojuen along with all the souvenir shops. There's an arcade just across the river from Kumamoto Castle. You can look into it from the streetcar from two ends. One of the first MacDonalds in the prefecture is still there (1981?), but there are many other choices.

Honmyoji is closest to Kami-Kumamoto Station, so be sure to get the B-Line streetcar as the A-Line goes back to Kumamoto Station and is much more frequent. The Shinkansen don't stop at Kami-Suizenji, so you might pick up a local 1 stop to Kumamoto Station and then pick up the Shinkansen back to Hakata.

Quick question here, and pretty dumb, but are the trams bi-direction, or strictly going in one direction only? I wanted to do the following order

Suizenji - Kumamoto - Honmyoji

Since Honmyoji only opens at 9am, so... yeah. Sorry for being so dumb, but the map doesn't really state if they go in both directions.

... I just realized the stupidity of my own question. Kind of figured it out after a while, please ignore the previous post. thanks to all who have helped though =)

Both lines use the same track from about 7 to 26. The only difference is when a B-line car gets between 7 & 8 heading toward Kami-Kumamoto, it switches off and goes straight while the A-line cars will hang a left. If you get on an A-Line car heading toward Kumamoto Station but want to go toward Kami-Kumamoto, just get off at Keitokuko-mae and walk to B9. Only B-line cars will be on this track.