Firstly Swansea is one of the best places for medicine in the UK and has many options like Genetics and Applied Medical Sciences in their medical schools but I know nothing about this specific subject. All medicine school subjects are held in the traditional Singleton campus. I dont know anything Edge Hill but I suspect it is on the outskirts of Liverpool so likely to have outstanding transport and nightlife facilities which will probably about the best anywhere.
As far as Swansea is concerned there are regular train links between Swansea and Manchester and London. Both are hourly services, The Manchester train is a small one and takes 4 hours via Crewe and Cardiff and has loads of stops. Once here there are regular services linking the station and campus. The buses from Campus to city take about 10 minutes and go about every 10 minutes day time. There is a night bus but it isnt every night which links both campuses and the city cenre.
In terms of nightlife Wind Street is very well known but obviously being a much smaller city than Liverpool there wont be as much variety. There are a couple of theatres and cinemas and there has been a new Arena opened this year.