In my opinion, this is the most exquisite and attractive United States coin.
2 pics below, obverse and reverse. This is a $20 Saint-Gaudens Gold Double Eagle. The one shown below can be bought for around $4,500 at today's gold prices.
Per the JM Bullion website:
During his presidency, President Theodore Roosevelt visited a renowned exhibition of ancient coins at the Smithsonian and what he saw inspired him to promote a new era of coins for America, coins that would reflect the grandeur and greatness of the nation. The resulting $20 Saint-Gaudens Gold Double Eagle Coins, designed by the celebrated sculptor Augustus Saint-Gaudens, has since become one of the most beautiful American coins ever minted.
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I appreciate that you included the background information as well.
but it's only the most attractive if you don't count this one:
my earbuds. I can't be bothered buying the high-end ones.
Honestly, I don't know the origin of those coins. Just looked for some ugly ones via a Google picture search.
P-E-N-
Never mind!!!
Who hacked into LuckyCharms' DU account? I want the nutty character back!
It's been one of those days. 
Also, I'm a numismatist...it's a longtime hobby of mine, so I geek out over coins. 
Mine are silver. They are my favorite. My husband got me a newly minted one for Christmas one year
I have a 2001 Walking Liberty. Sorry for the confusion.
American Silver Eagle. Worth about 90 bucks each. But the sentimental value is priceless!
Edit to add: I buy 3 of these every Christmas for my friend's 3 kids.
A long time ago, before the Internet, one of the local newspapers had a trivia contest. Person with the most correct answers each week won a silver dollar. I won several, then the paper limited it to one per person. It was fun while it lasted