if you're somewhat familiar with electronics repair, you can do it yourself, there are online manuals how to do this and the hinges are like $3-5 apiece. Still if you're not sure what you're doing, don't. You can easily damage LCD cables, so you'll have to get a new LCD module.
I replaced the entire shell for my DS phat after breaking a hinge, wasn't too hard at all. My gf currently has a cracked Lite hinge, but she refuses to let me touch it -- if there's a cost effective repair service for this, that'd be neat.