My question is this: How do I give my players direction, have them make their own direction, and make them involved while keeping a sandbox style game? How do I make this style of game fun for my players?
First, as many other folks have mentioned, it's probably a good idea to have a good conversation with the group about what kind of game you run and what you're looking for. "I like to have an open world with a lot of stuff going on, but it's up to you pick your goals and directions within it." If that's not what the players want, there's nothing to do except find a different style of game or different players who want what you offer.
Second, maybe point out 3 locations with known problems going on and ask the players during character creation to tie their characters into 2 of them. You may want to also change your reward system a bit so the players are rewarded with XP or whatever type of points when they pursue their goals they've established. As play goes on, allow them to change those goals or replace them.
Explain to the players, "I build my game around YOUR goals. So you may be on the way to do a mission and run across a few other things along the way - it's up to you whether you're going to sidetrack or not and what comes of that. That's not me telling you to definitely go one way or another. I present some choices, but it's you who make them."
Finally, be sure not to OVER-prep. It's easier to have a flexible game system that makes it easier to improvise than it is to spend lots of time writing up stuff that might not see use and even more so if the players aren't really into side-tracking.