Sharlene, the Monday-Monday aspect is excellent. That will give you plenty of time to see everything. The lack of car, though... not so great. As I said before, though, it's going to limit the NY style places you can get to.
Scott Wiener is one of the area's greatest historians. If the history is important to you, I'd definitely do a tour. If consuming the area's best possible pizza is your goal, then I might skip it. You couldn't pay me to eat at Lombardi's. And Joe's is pretty nondescript these days. If you're down at Keste and want to grab a slice at Joe's, sure, but I don't think it's worth a stop on a tour.
Coal oven pizza can be very inconsistent. The oven temps are hard to control. There's also, I think, in the case of places like Lombardi's and Totonno's, a lot of apathy/resting on laurels. No matter where you go, it's going to be a gamble, but I think you should experience at least one coal place. I don't think it should be John's. I've never been to Patsy's, but, after reading countless reviews and tracking their progress over the years, I think they show the most promise.http://slice.seriouseats.com/archives/2011/08/nyc-quintessential-patsys-pizza-east-harlem.html
The one thing besides history that Scott Wiener might offer could be some VIP treatment. Eating at Keste- nice. Eating at Keste while conversing with Roberto- amazing. If Scott can guarantee some Roberto face time, then that might be worth it.
Speaking of apathy and coal, I just noticed that Patsy Grimaldi's new place has opened.http://www.julianaspizza.com/
I would definitely
add this to the list. Patsy's getting on in years, but he has a lot to prove, and Craig's buddy Matt Grogan, a self professed 'pizza nerd,' is running the place. You're not going to find any apathy here.http://newyork.grubstreet.com/2012/10/pizza-legend-patsy-grimaldi-gets-his-good-name-back.html
Slice, amazingly, hasn't reviewed Juliana's yet, so, if you go, the obligation for feedback will be very high
This idea is pretty far out there, but, with a week at your disposal and your passion for wood fired pizza... I might consider contacting Giulio Adriani at Forcella and see if he'll either let you shadow him for a day or two and/or give you a training session or two in the mornings. Giulio's a VPN instructor, and, while you can't take a whole class with him, any kind of one on training/shadowing would be beneficial to your craft. I don't know what you'll do with the kids, but I think you could get a tremendous amount of knowledge out of this. You also might want to see if you can contact Roberto as well. Roberto has been incredibly busy, so he's probably not doing anything along this vein, but, you never know. In addition to Roberto and Giulio, you can take a train out of the city that will take you right across the street to Amano. Roberto won't be there, nor will there be anyone of Giulio's caliber, but, out of all this list, the guys at Amano are the friendliest and most likely to be open to training/shadowing. As Craig said, it's one of his favorites in the area, so there's definitely knowledge to be learned there. Training/shadowing at Amano also might not be quite as expensive as what Roberto or Giulio might charge you. If you're interested, I would touch base with Carlo at Amano, perhaps through John Conklin on this forum, who knows him well.
One last option, a bit of a long shot, is see if Roberto's daughter (now in charge of Keste) will train you. She hasn't been doing this all that long, but I still think you could learn a lot from her.
Roberto and Carlo (and most likely Giulio) are all part of the ambassador, open book, education trumps propriety business knowledge mentality. They have no secrets when it comes to pizzamaking. Paulie would be fantastic to train with, but he guards his secrets like Fort Knox. If he trained you, he'd have to kill you
Bottom line, while you're here, I really think you should try for some form of training with someone. You might be able to find an au pair with impeccable references to watch the kids for the day(s).
Even if you skip the training aspect, if you can find out where Roberto will be at a given time, I'd try to meet him in person. I don't know how much time Don Antonio is spending at Don Antonio, but, if you speak Italian, he'd be a massive resource.
A train and a cab will get you up to Johnny's in Mount Vernon. It's going to take a chunk of time, but I'd definitely invest it. You can probably do Patsy's at the same time.
Vesta (East Rutherford) has a bus stop a block away for a bus that goes straight into Manhattan. Craig has taken it and can vouch for it's ease of use.
As I mentioned, there's a train out to Amano in Ridgewood. That's going to be a long ride, though. If you're training out at Amano, then I'd definitely take the train. To go that far of a distance to eat a meal, that's a tough call.
Williamsburg pizza is a very well received up and comer, but you'll need a real NY slice beyond that. New Park is kind of out in the sticks, but accessible by bus and train/taxi. The bus, according to google, from Murray Hill, is an hour. I'd save some time and take the 7 train out to Brooklyn, getting away from some of the congestion of Manhattan, and then taking a taxi from there.