When my girls were really little, I didn't want to bother with messy dyes, so we would use markers and stickers. One year, we rolled the eggs in white glue and then in glitter and let them dry. Those turned out really pretty. You could also cover them with tissue paper for a stained glass effect.
My mom used to prick a hole in each of the egg, blow out the insides, clean with water and let dry. You can then paint the egg for a pretty, though fragile egg. Not good for egg hunts. It is only as a decoration and will eventually break. However, it is less messy than a real egg that can get lost and smell.
Also, consider plastic eggs. You can decorate those with stickers, paint, etc. and no worries over losing and them smelling later on. I mention that because we always had at least one egg we could never find after our hunts.