First I would print out the discount codes from Theatermania or Playbill (not always the same shows offered) for any show you may be interested in. I'm assuming since you have limited time you don't want to spend it waiting hours in line for TKTS, Lottery or cancellations to shows that will be playing for a while to come.
Sunday night - MUSICAL OF MUSICALS
Monday night - CHICAGO
Wednesday matinee - 12 ANGRY MEN ... a must see. Try for good seats with the
discount code. If none available go for the rush seats near the rear mezz for a
fraction of the cost - something like $26.
I think both you and your dad will enjoy these shows. And I would pick 12 ANGRY MEN over DOUBT because it is a limited run. It is riveting. And your dad would probably remember he enjoyed the old movie or TV remake. And you don't see shows with this large a male ensemble, and this well acted, done often.
And yes, go to Rockerfeller Center. If you don't want to do the NBC tour at least check out their store. Bet you'd enjoy hosting The Tonight Show, or Late night, or doing the Today Show weather forecast.
Check out the shops in Times Square. Go to Toys-R-Us and see/ride the ferris wheel. Go to the TheaterCentral shop near The St. James theatre. And visit the book store in the rear if you're looking for a play. Then have a least one meal at John's Pizzeria just to check out the converted church. Go to the Drama Book Shop.
Bye a copy of TimeOutNY and see what events, tours, exhibits, shopping adventures, comedy clubs...will be available while you're there. See what's being shown at the Television & Radio Museum. It's often something theater related.
Rest in peace, Iflitifloat.