Your calculations are correct as far as they go. But.
First, the "normal" way to do this is to use a 12-volt battery to match your 12-volt array. The output of the battery would feed a 12-volt to 5-volt DC-DC converter.
Second, you have not factored in bad weather. If you don't want a cloudy day to kill your system, you must factor in a margin of safety, since after 1 day you'll have used up all of the previous day's energy, and if it's cloudy you won't get a full day's charge. How big this margin needs to be depends on exactly where you live and how much risk you're willing to take. Let's say you size the system to allow for 2 cloudy days in a row. Then you need to provide 3 times your base power, or about 200 watts from your PV cells. And frankly, I'd consider 60% system efficiency optimistic.
Third, your battery must be much larger than you probably realize. 240 Wh from a 12-volt battery is 20 Ahr. 3 days capacity is 60 Ahr, which is about the normal size of a car battery. However, if you're using lead-acid (they're cheap and the charger techniques are easy) and you want them to last a long time, you can't fully discharge them. In fact, for regular lead-acids, you should not discharge below 80% of charge. In this case, you need a battery 5 times larger than you thought, or 300 Ahr. If you're willing to shuck out the up-front costs, you can go with deep-discharge marine batteries, and you can live with a limit of 50% discharge, for a 120 Ahr system. But again, this assumes you're willing to live with a certain level of risk. Bigger battery = longer duration = higher price and larger size.
Finally, check the rules. This is not a product-recommendation site. Develop your Google-fu.