I'm all about having a dedicated site for your band (*cough* bombplates.com *cough*). It's good to have a hub where users can consistently find you as the various services and social networks rise and fall.
Mostly, you just want to get your own domain name so that you can move it from service to service. Whether its a tumblr, dedicated site, Facebook, whatever, you want people to always be able to type in yourband.com (or Google you) and get to your band.