You're missing out Kenilworth, which is increasingly popular. Verrrrry nice area. Also Canley/Tile Hill, which allows you to walk into uni.
I lived in Leamington in second year (with Warwick Accommodation) and the houses aren't bad, but OH MY GOD the pain of waiting for those buses in the pissing rain and the cold. The times that over-full buses just passed you by. The times the same thing happened when you were trying to LEAVE campus and it was dark. Eugh.
There's also nothing happening in Leamington. It's essentially just a few nice restaurants, a naff shopping mall and a couple of supermarkets, so you have to get out to do anything/not go mad.
In this respect - unless you're up for heading into Birmingham/London regularly - Coventry is much better as a place to go, just not necessarily as a place to live.