I did want to follow-up on this thread.
First, thanks to everyone who contributed to helping guide our trip. It was incredible and we did things we otherwise, would not have.
Enzo: The japan-guide site was incredibly reliable and helpful. Kyoto was on the list, but was cut. I think we could have spend a month in Japan and still not covered enough. We ended up anchoring in Odawara, instead of Tokyo. Our biggest problem was hotel space. Most Tokyo hotels only allow for 3 people. Odawara Hilton Resort & Spa allowed capacity for all of us in one room. Expensive... but worth it. We had concern about traveling distance (say Tokyo to Nagoya). Once in Japan, I could totally see what you were saying about anchoring in Tokyo. It would have been fine.
Since we had more than 4 people, a single box was not enough. We got a box and then stadium seating. As we entered the arean, the boys taken and were escorted to their seats. I handed them a 50K Yen and told them to be good, not knowing where our seats were. We all had a great time and they loved not having mom and dad lord over them. I would have NEVER done that for a sporting event in the US. Give my kids tickets and then not have access to them. It was great.
We didn't make Fuji-Q/Mt Fuji, either.
Regarding budget... We were in over $20K before we even started packing. Between flights, hotels and rail. It added up. We did stay below my most high limit... by about $150. But we did a ton of stuff and it was WELL worth it.
Silky - The Tsukiji Fish Market was excellent. It will be moved, as it is the site where the Olympic Village will be. We did an insider tour and sushi making/sake tasting event. It was incredible!
Random - We didn't do the tuna auction, but I wanted to. It was just too early for us.
AggieMainland - We did a similar tour. I had looked at the one you linked, and for whatever reason, when I finally booked, we selected a different host. It was awesome, though.
BackwardsInBoots - Thanks for all your help. We had Kabuki-za as a general think to look for. In Nagoya, we stopped at the Nagoya Noh Theater by the Castle. It was a good easy win. The JRPass was absolutely necessary for us. It was great. You have to get the certificates before entering Japan. We almost missed that. We got the 14 day pass, for like $425/person. We went from Odawara to Nagoya twice. One way was $93 (or so), so that was $372, just spent there. We did parse down expectations. No Kyoto. No Nara. Being in Odawara, we went to Hakone. They have an all-travel pass for 2-3 days. We loved the area. I did have the boys give me their "non-negotiable" things. We got everything except my wife's onsen experience. More something we'll have to do without kids.
Airbnb was just too risky for the overall budget. Having a restaurant in the hotel was expensive, but safe, when necessary.
I agree, the macaques are out of place and they look miserable.
FriendlyAg - My son had Akihabara on his list. We got passed the main area, and I was like, "Ok, so now what?!" It wasn't until we came back, that it was like, "Oh... I get it." We spent a bunch of time there and one found some "Monster Hunter" stuff which was great.
Seven - Didn't make it to Harajuku. We did try a variety of places at all price levels. Started with 7-11 at Narita Airport. We are pretty adventurous. My boys wanted ramen, so my wife found a local place in Odawara. We walked about 2 miles to this hole-in-wall place. It was like 800Y per bowl. We shared and it was awesome. We also found a sushi place. Neither spoke any English, but we did fine. The sushi place had English menus, but the Japanese menu had pictures.
We ate on the go and local as much as possible.
BlueAg - I've traveled many places, including NYC, Denmark, et al. For us... the expensive part was hotels. You have to book rooms by the person. Most hotels have twin beds, so you also have to pay per bed. Our stay in Odaiba was a Hilton property. We got a Triple Room, which had 2 twin beds. We had to get a roll-away bed for $70/night. It brought the total to about $500/night... and we had to have 2 rooms. Essentially $1K/night. In Odawara... another Hilton property... we got a Suite and paid for 3 futons in addition to the room. The idea of roll-aways are common... but in the US, you can usually get two Queen beds and share the bed. In both places we were, they were only twin beds. Rail would have been expensive if we bought individual tickets. But, at $425 for 14 days, we're looking at $30/person/day. Or... $2K+ for the trip. All-in-all for food and entertainment... I didn't find it unreasonable. But we drop $60 at home eating fast food. We can't eat dining for less than $125 and Sushi puts us at over $200 almost every time.
Random - Yes, tempura was popular. In Odaiba, they had restaurant in the Diver Mall, that looked like a fry pit at the table, where they'd bring your tempura raw and you'd cook it at the table. We almost did that, but just didn't fit.
Spore - Our hotel in Odawara ran a shuttle every 15mins or so to the Nebukawa station and our Odaiba hotel was on the station. Both were very convenient. I didn't find the 100Y beer vending machines, but my boys found the 160Y soda/drink machines. They really like the "gel" drinks and they knew they had me gamed. We'd go to leave the hotel and I'd tell everyone to get a water. "We're fine. We are not thirsty." 15 min shuttle to the rail station and suddenly everyone is about to pass out from dehydration. So, I kept a bag full of 100Y and 500Y coins... a roll of 1000Y bills. The down side to that was gasha-pons (sp). Man o man... THAT was a beat down. 100Y coins spend like quarters. "Dad, can I get a gasha-pon, these are the ones I've searched everywhere for. It is the only one I've found." They are usually 300Y-500Y, so now I'm dropping $3 on a McDonald's-type toy for each kid... and they are EVERYWHERE! I probably spent more on gasha-pons than I did hotels. jk.
Its Not Rocket - WE opted for Sky Tree. It was fantastic. Skipped Disney. Disney Sea seemed interesting, but didn't move the needle enough to displace something else.
Thanks everyone for your input. I think I covered everything. What would have been a really good trip, became a fantastic trip with less anxiety. Thank you!