My impression is that "hi, can I buy you a drink?" is cliché but I don't know what reasonable substitutes are.

"Hi, what's your name?" or "Hi, I'm Qiaochu" (depending on the cultural context, e.g. ISTM the former is more common in English and the latter is more common in Italian). Ain't that what nearly any language course whatsoever teaches you to say on Lesson 1? ;-)¹

Or, if you're in a venue where that's appropriate, "wanna dance?" (not necessarily verbally).

(My favourite is to do something awesome in their general direction and wait for them to introduce themselves/each other to me, but it's not as reliable.)

1. I think I became much more confident in introducing myself to strangers in English or Italian after being taught explicitly how to do that in Irish (though there are huge confounders).