I know how to wrap a figure with text and everything.
But where is the best place to put it? On the left? On the right? Any good, reasonable ideas about that would be very much appreciated.
I would say: it depends -- but you shouldn't wrap figures at all!
In a twoside document I would basically prefer them to be on the outside but I don't know if there is an automatism in
wrapfig to ensure this. Above that I wouldn't consider "on the outside" as totally fixed as it may depend of the structure of the text -- if you have a text with lots of short (1-5 lines or so) paragraphs it may be better to have the figure at the right border of your text area (which is then the inside of left pages). If the structure of the text allows it one could also try to move it to passages with longer paragraphs.
Unfortunately these considerations involve a lot of "feeling" that isn't easily expressed in algorithms. Therefore it would require a lot of manual work with shifting things around in trial and error. This is the reason why I think that such wrapped figures aren't a thing to be just set by using a package and thinking everything is fine. In my opinion such things should be done by someone who has some (professional) experience in typesetting.