Huffy Cranbrook 26" Ladies' Cruiser crank / pedal / chain "pop" sound...? Before you say it's a cheap bike, what more do you want... I get that! :D
But it's brand new, and as you pedal it... no matter the speed, you get a pop sound at a specific point on each rotation...

What could / should I do to help silence this sound and make the ride more enjoyable.

Please advise if you can!

VIDEO UPDATE:
I uploaded this video of the happenings ;)
My guess is that the chain is too tight. You say it is only at a specific spot in the rotation which leads me to believe your chainring being slightly off center (I have not found one 100% perfect) is causing the popping. 

Flip the bike on it's back and spin the cranks slowly. If it is a freewheel pedal, it backwards since this will not engage the sprocket. If it is a coaster, you will have to pedal it forwards. If you notice the chain get really tight then loose as you do this, adjust your chain. Find the same spot the pedals are at where it gets the tightest and loosen then tighten the rear wheel with the cranks in the same spot so that the tightest it will get is where you just set it.

If the chain tension was not the problem, you might need to check the bearings. Huffys almost never have sealed bearings and they can be over under tightened, either being a problem.