We went to 2 Jr. Days. Both schools were successful programs. Both followed a similar schedule. Start in the morning with about 25 kids and their folks, addressed by the Coaches, AD, radio announcer, etc.
Then tour the ball park, school, meet the academic advisor and eat in the athlete lunch room.
Yum.
Watch the game after lunch and go home.
You should try to attend if invited if you are interested, but if it's not feasable right now, just tell the coach. There is not much "one on one" stuff anyway so maybe an unofficial visit later gets more accomplished anyway.
I wouldn't "chase" a Jr. Day invite from a school. If you are getting Jr. Days invites, the right offer at the right school at the right time will likely follow. JMO