Late pre-hardmore is my favorite. I like that in this stage you don't feel completely OP with wings and insane weapons and all that - it's a lot simpler, and movement is more fun when you have a lot of options instead of just using your best wings. Flying carpets, grappling hooks, balloons, bottled jumps, rocket boots, the list goes on.
Early to medium hardmode is also very fun. A lot of biomes to explore, bosses to kill, events to grind and gear to acquire.
Now, my least favorite, excluding the absolute beginning, would be endgame right now. I'm sad to say it, but I think that the 1.3 endgame is really boring compared to the 1.1 and 1.2 endgames. In those versions, especially 1.2, to get the best gear you had to explore the entire world and you got to fight new enemies as well. Now it's just grind this one event and boss until you get the gear you want. It feels so meaningless.