Arriving in Beijing, leaving thru Hong Kong but the online visa app doesn't have a Hong Kong option!

Your departure city should be a foreign city out of China while HK belongs to China. You may put in the city in the USA where you set off initially. I'm a little confused about your travel route. You said you would depart from HK, if I understand it right, you will take a cruise in HK to Beijing, then back to HK for a flight at HKIA to leave? You will exit China after the 2-week cruise? If yes, I think you can put in 15 days or to be on the safe side, you can put in 30 days. The final duration is decided by the consular office according to your travel itinerary you submit.