If I understand you correctly, you will purchase a ticket to fly to Tokyo on ANA, and another ticket on United from Tokyo to the US. These flights will occur on the same day, but several hours apart.
With one caveat below, you should have no issue with checking your bags all the way through to the US from wherever you are originating in Asia. Virtually all airlines have <i>baggage transfer</i> agreements. Don’t confuse airline alliance programs or code sharing arrangements, where airlines share equipment and routes with certain airlines, with baggage transfer agreements in which they agree to transfer passenger’s baggage between them for free. (The only airlines which to my knowledge may not have this agreement is British Air for some UK transfers, and certain airlines within in India. In 20 years of connecting internationally in Asia, I have never had an issue with baggage transfer.).
If you are flying different airlines, you will not be able to get a boarding pass for the Tokyo-US portion of the flight from your originating airline, so when you land in Tokyo, the first thing you have to do is go the transit area and get a boarding pass for your onward flight. (There can sometimes be lines for this, but usually moves quickly.) Then you would proceed out to Immigration to go into Tokyo. You also have to go back through Immigration when you return, so build in time for this for your layover.
Most airlines only consider you to be “in transit” if your connecting flight is within 12-18 hours or so of your arriving flight. So if you have more time than that between flights, your baggage may not be transferred. The amount of time permitted between flights depends on the airlines, the airport and the fact that you are flying TO the US, where rules are often different and cut off times are often shorter. So check with the airlines and the website for the Tokyo airport.
In any event, there are coin operated lockers and a manned luggage room at the airport, see
http://www.narita-airport.jp/en, click on “Airport Guide” and then “Facilities & Services”. You may want to store hand luggage there.
I also would just mention that trying to “see” Tokyo on a layover may not be ideal. First of all, it is over an hour each way by train to Tokyo. Secondly, there is not a whole lot to “see” in Tokyo other than just the city streets themselves, which may not be a whole lot of fun. There are a few museums (not sure you have time for them, will they be open on your one day, etc), the fish market (only good in the very early morning hours, so probably you will be too late for that) and the Asakusa area and the Sensoji temple, which again you may not have time for. It does have some temple complexes but it really does not offer a whole lot in terms of cultural sights at least IMO. (Frommers #1 site recco is the fish market, that may tell you something.) Third, it’s a rather expensive city. Fourth, while the subway system is quite good (you don’t want to take taxis if you can avoid it because of the cost), it can be quite confusing to figure out, and I am not sure it is worth it for such a short trip. (I am not sure it is worth figuring out the train to the city from the airport for such a short trip.) I personally would not arrange a whole trip just to try to have 5-6 hours in Tokyo. You really won’t see the city at all. I would try to spend a few days in the city or skip it.