As we tell our kids, the only dumb questions are the ones you don't ask and thus never get answered.
The AF provides the appointee with a gov't ticket to get to AFA. If you want to go too, you fly in on your own dime. Flights to COS will be FULL on the 23rd so if you want to get there book asap. Odds of you getting on the same flight are slim - so you could fly earlier and meet them there. No planned activities on the 23rd unless they are a recruited athlete - usually the coach has a get together for the recruits the evening before I-day. Yes your child stays with you the night before I-day.
If you don't want/can't fly out with them, I highly recommend the Bed & Breakfast program the AOG runs. Your appointee signs up on AOG page, pays minimal fee (like $10-15) and will be matched with someone from the local area in AOG who will pick them up either at airport or AFA and house them for the night and then take them to Doolittle Hall in the AM the next day.
As for what happens on I-day -- I only have second-hand info as our son did the B&B program. I do know they go to Doolittle Hall, get a briefing, eventually go upstairs and get BCT squad info and then exit a different door, go over the bridge and get on the bus. Parents say goodbye to their children prior to them going up the stairs. They get to wave to them as they exit the bldg to go over the bridge.
Parents can hang around and watch from the chapel wall to see the appointees dragging their bags and maybe marching some the rest of the day; they can also meet other parents. There is no "formal" planning for the rest of the day, unlike WP & CGA (don't know about USNA).
The next day is the swearing in ceremony which parents can watch from the chapel wall.
Local parents will watch the march out to Jacks Valley and the march back later in July.
Acceptance Day is the other event of the summer some parents attend. It will be Aug 4th this year. There is a parade where the BCT grads are "accepted" into the cadet wing and get their shoulder boards. After the parade you get 2-3 hours with your cadet but you can't leave the cadet area so most people bring picnic lunch to share by the field house. You can also bring stuff to them then (computer monitors, printers, etc). We could not attend A-day either, but our son was "adopted" by someone in his squad and they fed him lunch and took pictures.
The event not to miss is Parents Weekend -- which is always Labor Day weekend. Make your reservations NOW if you haven't done that. Come in on Thursday and don't leave til Tuesday am. Thur night you can meet your cadet at the chapel or A-hall and bring them dinner. Events planned for Fri-Sun; cadets are released to you after the football game til 7pm Mon night.
Sorry for the long post.
Enjoy the ride and congrats to you & your appointee!