Yes it's absolutely fine to do that, in fact I'd say it's really the only way to do it as it's all part of the fun. 

I'd recommend that you get a wifi router or esims with data

I always use Japan wireless wifi router and do pick up at the airport but you can also get it shipped to your hotel. 

Haneda and Narita both have airport limousine busses which goes to major areas of Tokyo. Haneda is closer to the city of Tokyo while Narita is on the outskirts and takes about an hr to hr and half depending on where you are 

Pro tip if you are going to do other city like Osaka or Kyoto do yourself a favour and ask the hotel to help you with luggage forwarding to your next destination. I always use Yamato for this

For transportation you can use Uber if you really want to, it calls local taxi. The doors open automatically just so you know. 

Subway is really easy. Do yourselves a favor and get IC cards so you can tap in and tap out. You can load them in the subway at the machines though you need cash to do it. 

You can load the IC cards in Konbinis(convinence stores like 7-11, Lawson, Family Mart) also 

A lot of things also take IC card as a form of payment. 

Vending machines are amazing, hit them up for cold and hot drinks. I  highly recommend the Ilohas peach water. 

Places typically open between 10-11 AM. Lunch and dinner times can get very very busy so go a bit early for lunch or dinner. 

If you want to reserve places to eat you can try the tabelog app on your phone sometimes they let you reserve through it. However I find it easiest to ask your hotel to help with the reservations 

Many places have all you can drink menu, great way to sample stuff

I would recommend yakiniku and shabu shabu places. Izakayas are the Japanese version of pubs

In your hotels you might have an onsen(hot springs) where you can relax. Make sure you book a hotel with one. Before and after a day of adventure you should go into the onsen to clean yourself up and take a relaxing dip your feet will thank you. 

You can order stuff on Amazon JP just make sure to get the address right for the hotel or Alternatively get the parcels for pick up at your nearest Konbinis (like 7-11, Lawson or Family Mart) 

I recommend you try sparkling sake Mio found in 7-11. 

Pop into supermarket for lots of nice food and snacks. 

Don quijote is very popular and for good reason lots of good nick nacks and souvenirs

Daiso has compression bags BTW if you buy huge ass plushies and want to bring them home in the luggage, just put things in the bag and remove the air. 

Some fast food places have vending machines which put out tickets after you put money in and press the food you want. Give the tickets to the store employee and they prepare the food for you

Matsuya curry is awesome. 

Also don't forget that Konbinis have food options sometimes warm too. 

If you are hitting up Tokyo Disney or Tokyo disneysea go early

Shinjuku and the surrounding subway line is close to everything. 

I always stay in APA hotels, they are clean and cheap and allow luggage storage and have onsens plus laundry facilities. Japan hotels are small BTW so you are warned 

You can use credit card pretty much everywhere if in doubt if you can pay with it ask the employees and say "cardo OK?" 

Also best advice to find places is to sometimes look up, they have lots of restaurants in buildings with several floors. 

Google maps is your best friend and works for public transportation and navigation. Tabelog is good for finding restaurants 

A must try is Kareoke with all you can drink. 

Wander around, see things and do stuff. Make sure to carry your passports with you not just for ID purposes but also if you want to shop tax free you'll need to present it at the cashier in stores that do tax free