Not a JMU student, but we share the private halls in the city centre. So I may be able to help.
Grand Central is nice, but there is a risk that you'll have the train departure announcements every 5 or so minutes from about 0500 until 2300 :P. But it depends which rooms your in. Also, maybe not a huge issue, but it's an uphill walk to the John Foster building (which as discussed is up Mt Pleasent near the University).
The student village (up near JMU students union and the Font bar) is quite nice (and being a student village is gonna be quite lively), but fills up very quickly, as there's no priority to JMU (so University of Liverpool, JMU, LIPA and the Liverpool Community College are on equal footing)
Liberty Park is another option, I absolutely hated it (but that was more due to my flatmates), but alot of people who were there last year are still there (which says something), most flats are JMU.
Prospect Point is also viable (near the hospital), though it's a bit more of a walk to the Foster building, but there's plenty of takeaways there etc. But it gives priority to the University of Liverpool's faculty of medicine students.
Another one I dont really know much about is North Western Halls, it's near Lime Street, but away from the open end (so you dont get the announcements)
The Student village and Grand Central are good, but expensive (I think GC was verging on £80 pw).
Liberty Park is alright, just a bit old fashioned compared to the other Liberty Properties.
The best thing to do is once you've got a place confirmed, head up to Lpool and have a look around the accomodation. A good website to look at is:http://www.lsh.liv.ac.uk
click on "Larger Properties"