DH and I met when he was at Warwick University and I was at Coventry (then still a Polytechnic). That was 40 years ago.
Our eldest DD also went to Warwick, graduating in 2017.
Warwick University is pretty much smack in-between Coventry and Leamington with very regular bus services to both. The campus has a lively Student Union, a sports club and the Arts Centre (Butterworth Hall etc.) where loads of events take place including performances from actors, comedians, music recitals (pop and classical). You name it. I think it has a cinema there too, or did back in our day.
The social scenes in both Leamington and Coventry are also quite lively. Leamington in particular has a number of clubs, pubs, bars and cafés. Lots of students from Warwick University rent there during term time. My DD house shared there with her friends and had a great time. All had met in hall on campus during the first year. No issues getting to campus when they wanted or needed to.
Who has been advising you that it is problematic? It isn't.
Just to add, if a visit to a bigger city is required then Birmingham is not that far away and easily reachable quite quickly by train from Coventry (maybe Leamington too as it does have a station but I am less familiar with that one).