As a fan of Calvino I will say that If on a Winter’s Night a Traveller is somewhat more enjoyable after you've read a bunch of other Calvino, since it has a somewhat cheeky, self-referential feel and the more you sympathize with the author the more you may like it.
Numbers in the Dark is very good as a place to start.
Marcovaldo, Cosmicomics, Difficult Loves are my favorite. Baron in the Trees too.
I'd definitely suggest starting with these. His short story work is beautiful.
I absolutely loved Invisible Cities, but I couldn't get more than a couple of chapters into If on a Winter's Night. The first pages are very evocative, but it gets really repetitive with nothing to "progress" the "plot".
My impression (possibly mistaken) is that it's a product of its time that was innovative, but hasn't aged that well. More a fun puzzle box than something with emotional weight.
Given the above, what other Calvino work might appeal more to someone like me?