Official Visits?

OK, found part of the answer. Kinda strange though:

As an NCAA rule, D1 and D3 schools do not allow tryouts. On an official or unofficial visit you may participate in workouts that are not organized or observed by coaching staff. They must not be designed to test your athletic ability though. D2 schools are allowed to conduct one tryout in the off-season of your sport.

Jjin,
Official visits are paid for by the school. IMO, it's NOT appropriate to ask for an official visit UNLESS you feel that the coach has been wooing you with all the tricks in the book except paying for you to visit the school.

It is appropriate for you to suggest an UNofficial visit. This is where you make an appointment to meet the coach, and maybe he offers you a tour, introduces you to players, academic advisors, etc. At an unofficial visit, he can't even buy you lunch.

Officials are paid for by the school, if a school is that interested in you they will ask you if you are interested in taking an official visit. Usually its on a weekend, the recruit will be paired up with a current player and they will basically hang out over the course of the weekend. Parents will be given tours of the grounds and facilities by the head coach or an assistant, and will answer any questions. Depending when the visit is, you will also get to see a game, be it a football or basketball game.

If a school is interested in you they will offer an official visit. IMO it is a bit to forward to ask for this, even if you feel you are being actively recruited.

But I feel you can try and see the coach while you are visiting campus on your own. Call and express your interest in the school and the baseball program. Tell him you would like to set up a time to see him while you are visiting the campus. Many coaches will go out of their way to try and see you.
Although, this may not be the case, or work with some of the more competitive baseball programs.