I don’t understand the meaning of this sentence: "In many countries, few things will ingratiate you more with your hosts, for example, than things connected with the ‘beautiful game.’
Thank you for your time!

“ingratiate you with your hosts” means cause your hosts to be pleased with you, and to think favourably of you.

It is saying that one of the best ways to achieve this is via things connected to the “beautiful game”, which means football (soccer).

I always feel that “ingratiate” has a negative nuance, so it’s probably not a word I would use here. Other people may have a different opinion.

I agree with Dozy. To me, ingratiate seems to imply some insincerity.

‘Ingratiate’ certainly seems to me to imply that the person ‘ingratiating’ considers himself to be inferior.