Hello everyone!
I'm Italian and I'm thinking of going to England next summer to do an English course. I'm going to stay there for 3 weeks and I can decide in which city to go among Cambridge, Bournemouth, Liverpool and Manchester. Which do you think is the best for a 18-year-old girl? I don't want to spend my time drinking or at the disco but to go in a place where there are a lot of different things to do (Shops, cinema,...). Also I'd like to go somewhere there are people my age.

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Doesn't help OP's English though

I'd say either Bournemouth, which is a trendy place nowadays full of younger people, or Cambridge.
The accents of the other two can be hard for other Brits to understand, never mind foreigners.

The OP's English seems to be very good. I am not familiar with Bournemouth, but I'd probably recommend Cambridge. We have a number of British friends and acquaintances from Manchester, and a couple from Liverpool, here in the Dordogne, and we find them virtually unintelligible.

Cambridge IMO for sure - lots of folks your age - very safe city - and lots of cinemas and things to do. Not a small town nor huge city. And easy to go to London on train for weekends - just an hour or so.

It’s been decades since I studied in Cambridge so take my words with a grain of salt. Won’t be many Cambridge undergraduates if any during the summer as the term ends with exams in early June and the Michaelmas term does not start until October. Tons of tourists during the summer. There used to be several English language schools near the train terminal which were a source of attractive young ladies. Cambridge was predominately male during my days. Easy to get into and out of London for a day. Don’t know if they still have discounted student day return tickets. Do not know much about your other choices.

Cambridge probably has more English schools than the other cities so will be more folks your age from all over.

nd saying 'Studied English at Cambridge' sounds better on CV than at other places!