Crosby Resident here, as mentioned above, Crosby, Formby, Maghull, Ormskirk all nice areas to Live, but not ideal for a student, away from Uni Campus & social circles that come with student life, not recommended on this occasion.
I would also rule out the wirral, not worth the effort & the additional costs of commuting will be noticed by a student living away from home
Good advice about south of city centre / sefton park above, but Im going to recommend Living in the city centre itself. I used to Live in a new build tower on the waters edge, city centre, not cheap ill grant you, but nowhere nice is! there were quite a few students in our building but we never had any trouble, secure parking, 24hr concierge! if i was a student in Liverpool now, its where I would look first!