It may sound odd, but I'd recommend buying an Android smartphone and throwing in a 64GB (or 128GB) microSD card. There are many good quality Android phones for prepaid systems that don't require cell service.
For example, BoostMobile and VirginMobile has the Sharp Aquos Crystal, a bezel-less handset with a 5" screen. It's a real looker and only $150, no contract.
I've take numerous Android smartphones and turned them into a media player. They can be used fine as-is as a media player (just turn on airplane mode) but if you are tech-savvy then you can root the phone and remove the phone bits and get even greater performance and battery life.