Hey there,
That's a great set of questions and I wish you the best of luck with that GMAT - I know you're going to rock it so the top 15 will totally be within reach! To your questions:
1) Should you wait? Well that depends on what you want out of your visit. If you want to get a better feel for the programs to figure out WHERE to apply, then no, you shouldn't wait. Because then you won't have enough time to put your apps together. But if you're going as just another data point and you're already pretty settled on your list, then you COULD wait. But what I would caution on is that a school visit is really just one way to research a school. You should be talking to students and alumni throughout the summer anyway. If you decide to go in the summer, no worries - every program holds info sessions and panels, etc. during these months so you'll still get a good idea. You'll just miss out on a) the class visit and b) the general vibe that you can observe.
2) Does visiting help? Of course it does. Some schools care more than others, but it shows interest. And in a world where schools worry about yield rates, they view you as a bit more serious. If someone else is reading this and you're international, that may or may not apply to you. But if you're in the US, then you should visit. A $500 trip when you're thinking about spending $135,000 isn't all that much. And you wouldn't buy a car without test driving it, would you? So does it help? Yes. Will it make or break your chances? Probably not. But it sure doesn't hurt!
3) Should you visit before applying? Yes, see #1 and #2 - visiting after you apply is a different ball game altogether. Not only do you not show your dedication in a timely manner, you also can't incorporate your learnings! So if you're going to visit, visit before you apply.
We've got a video on school visits - it's short (few minutes) -
you can watch it here.Don't forget to explore the city in addition to the school - you'll spend 2 years there so make sure you'll like it. Good luck and have fun!
Bhavik