In Japan, there are many odd (and sometimes unintentionally hilarious) signs with translations of Japanese phrases into English. This is a good example, as "please smoke with good manners" is not at all idiomatic. A more idiomatic version might be:
Please be considerate of others when smoking in the area surrounded by planters.
Please be courteous when smoking in the area surrounded by planters.
Side note: One of the funniest "Japlish" signs I ever saw was from a train station, which advised passengers:
Please do not run into the train.
Good advice to be sure, but more likely they meant to say
Please to not run onto the train. / Please do not run to get on board the train
Logically, "into" makes sense, but unfortunately the phrasal verb "run into" something means "collide with", usually "head-on". I suspect most people know it's not a good idea to run into trains.
(Edit) For general interest: A direct translation from the Japanese マナーを守って (mana o mamotte) would be:
Please mind your manners when ...
However this is somewhat too strong for a public sign, as it's the kind of thing parents might say their children, or a teacher to her students.
Now children, be sure to mind your manners when we are at the museum, otherwise they won't allow us to come back.
A more nuanced translation would be "be courteous".