u/gc1

I don't really see the appeal of Shibuya Sky and similar attractions. I certainly wouldn't spend money or line-waiting time on them. Many tall hotels, including the Cerulean Tower, the Andaz Toranomon Hills, and the Conrad Tokyo have rooftop or top floor bars with good views. They're not that amazing. The view of the Shibuya scramble from Starbucks is great and free.
A lot of the famous shopping areas got old quickly, e.g. Cat Street was not that interesting. If there's a Fjallraven, a Nike store, a Converse store, etc., these are all things you can find in west LA or Park City Utah. While there are only-in-Japan items at the big stores like Uniqlo, these stores (and Muji, Daiso, etc.) exist everywhere and it felt like monoculture to me when people I was with wanted to spend time at these places.
By contrast there are lots of interesting Japanese designers and bespoke clothing makers and such. If you're going to clothing shop, do some research (e.g. on r/malefashionadvice) and map these out in advance.
Also, Hands Tokyo (and Hands Kyoto), along with Itoya in Tokyo, were interesting, if a little chaotic, if you're into stationery and similar stuff. Great places for gifts like models and paper crafts.
By contrast to shopping, I really enjoyed walking around some of the lower-rise neighborhoods more than I thought I would. Wandering random back streets from Shibuya through Daikonyama and Nakameguro for example was really nice. So was Komagome and the Rikugien gardens. I kept wanting to put my camera to my eye to capture the interesting housing, architecture, found landscapes, and abstract compositions. And of course you stumble upon interesting shops and restaurants in these neighborhoods.
We didn't do any luggage forwarding, but after hauling bags up and down stairs in the big stations, while also wearing backpacks and carring bags of bento boxes and train supplies, I get the appeal. It takes some planning, but if I went back again, I might set it up differently, with a bigger piece or two of luggage as a "main supply" for sending ahead, and a smaller/weekend back for the night or two after the luggage is sent and/or before it arrives.
Similarly, staying at a higher-end hotel, something we did mainly because of points etc., allowed for the convenience of using the bell staff to get your luggage and load it into and out of cabs for you. You really don't have to touch your bag between destinations if you don't want to.
In Kyoto, Fushimi Inari and Kiyomizu-dera were absolutely stunning and worth it. I see lots of debate about this and think there shouldn't be any. Do them both for sure.
It wasn't always easy to find good meals quickly. We were traveling with a teen who was subject to suddenly being hungry. In both Tokyo and Kyoto, we had trouble manifesting good food without advance reservations or long waits. Plan ahead, or don't be picky. By contrast, at off hours, and not insisting on the very most popular spots, there's plenty of great food around. When in doubt, just get ramen or yakitori.
Kyoto in particular was horrendously crowded in the tourist areas like Gion. We found better food in quieter parts of town across the river. The shrines were crowded too, but we went early enough to beat the worst of it.
We did one fancy omakase. It was good but a lot of food and not really worth it. I'd rather have spread the calories and yen out over multiple smaller or more interesting places.
Good third-wave coffee shops and bakeries are around and worth sniffing out.
Whoever told me not to bother bringing a water bottle was absolutely right. I took one but used it only in the airports. It was just so much easier to tap suica on a machine and get an 80-cent bottle of water when thirsty than to find refills and carry weight around all the time.
I ended up going through a lot more Suica and cash yen than expected, and kept having to help the wife and kid top up to get out of train stations. Next time I will just load them up at the beginning and let them buy stuff to bring home on the last day or at the airport with whatever's left.
Teamlab was a cool experience, but just ok to me. It was quite crowded, so not exactly a meditative, transforming experience. I'd do it lacking anything better to do, but I wouldn't do it at the expense of other only-in-tokyo types of experiences and honestly wouldn't burn half a day on it.
I wish we'd done a little more museum art and artifacts, and a little less shopping.
Shinkansen stuff was really easy. Definitely worth the trouble of connecting Suica/IC card profiles into SmartEX to be able to simply tap into the Shinkansen turnstiles. I do wish smartEX didn't log me out all the time and was glad I used a memorable password.
The Eki stamp thing is really fun; my teen really enjoyed the hunt for them and building up her book of stamps. Allow extra time to find the stamps at train transfers, which can be pretty stressful when under time pressure.
Hakone -- everyone talks about the romancecar from Shinjuku, but I found the the Odakyu line from Hakone-Yumoto up to Gora to be the most interesting part (and way more interesting than the bus on the same route), including the cool way the trains change directions to feather up the mountain. This allows you to take the bullet train to Odawara and switch there or at Hakone-Yumoto. Try to sit or stand in the very front or back. The Hakone Open Air museum was pretty cool and worthwhile.

A few takes after a first-time visit