はしご酒をするって英語でなんて言うの？

A pub crawl is simply the action of moving from one place that serves alcohol to the next. Usually after taking one or two drinks. Crawl is not really showing action here as you would not usually be crawling. but more likely speed as it is done at a slow pace.

Many times, going from bar to bar, pub to pub, is perceived more as an action rather than a thing. Hence, the term "pubcrawling" is more appropriate. It also applies to the social activeness that is associated with bars and pubs. "Frequenting bars" is more official as citing this activities in a professional way. It's a term one might use when writing a police report. ex. "The assailant was noted for frequenting the bar in question."

Barhopping is one way you can say this. It doesn't mean literal hopping on one leg, rather implies moving quickly from one bar to the next. In Britain this can be known also as a 'Pub-crawl'. This is where you go from one pub to the next and the crawling implies that by the time you get the end you will be intoxicated. Some people do this on a night out so if you were to say a night out they would assume you were going to multiple places.

If you go from one bar to another for drinks then you can use the terms 'Bar hopping' or a 'Bar/pub crawl' these both mean the same So you could say 'We went on a pub crawl last night' or 'We went bar hopping last night'

In my area we usually say, "Would you like to go for a drink?" or "How about going out to get some drinks?" to mean that we are wanting to get some alcoholic drinks. If you say "Lets go clubbing" or "Do you want to go clubbing?" then that means going to a couple of different clubs or bars to drink and dance. That way you are not stuck at one bar or club. You often go to different ones depending on how exciting or fun they are.