I have a pretty reasonable grasp of delta V. While my comment is flippant, you can launch Eastward from the equator any day and end up in space: deep space if you have sufficient velocity (though usually you'd do that with one or more gravity assists). The sun is the only other place you can go any day, but there's huge angular velocity to overcome to make a direct shot.

It really really is the case mathematically that if you just want to go to deep space it's not as difficult as trying to figure out how to go to a particular place, as anyone who has ever done trajectory planning with STK will tell you. More difficult from a cost and engineering perspective, sure, but mathematically easier to just shoot in a direction at escape velocity for the sun whatever day you want.