You would have to be with him as the age requirement at PI is 18 and older, unless accompanied by an adult. Comedy Warehouse is much like "Whose Line is it Anyway" with Drew Carrey, it can be kinda rowdy but definetly something that he would enjoy (just remember that there might be some language as it is geared to adults...but in my expereince is not usually that bad). THe Adventures Club is a favorite of most CM's as it is just a fun place to go. The show in there is very off the wall but so much fun.
The Comedy Warehouse shows are
Sunday-Wed 8:20, 9:15, 10:30 and midnight
Thursday-Saturday 8:20, 9:15, 10:30, midnight and 1am
There is usually a line for that so you would want to get there early to get in.
Adventurer's Club showtimes are 8:15, 8:55, 9:45, 10:25, 11:05, 12:10 and 12:40am this is more of an open seating and not usually to crowded.
If you do go he would not be able to go into Mannequins (anytime) and the BET Soundstage (Fri or Sat...any other day of the week is ok) as these two are 21 and older and check ID at the door.
As for food there really is not "food" in PI but you can get soda and non-alcoholic drinks at any of the clubs.
On your question for what day of the week Monday and Thursday are Cast Member nights so they tend to be very busy and a little more rowdy and risque, any other night is hit or miss depending on the time of year... Just remember you would need to be with him for him to go...I have seen little kids there so I would not worry about a 6 foot tall young man looking out of place
