Which is better grammar: "courteous of" or "courteous to"?

"Courteous to others" is correct. "Courteous of others" is possible, but the former is more common.

"Courteous to others" has 483,000 results on Google vs. "Courteous of others" which only has 85,400 results

For the most part, the two phrasings are indistinguishable, but I believe there are subtly different implications between them.

Please be courteous of others is advice to be taken "inwardly"; it is advising its recipient to be mindful, to think of the actions that others might take. In particular, there is a mental component to the prescription; it says, you should think of others' desires before doing whatever it is you want to do.

Please be courteous to others is advice directed towards "outward" behavior; it advises its recipient to simply act courteously, not necessarily think so; it says, you might think as rude as spiteful thoughts as you want, but please observe a modicum of politeness.