I have a 1oz. American Eagle $50 gold coin. It is in perfect uncirculated condition, but I'm not sure how much that matters, as its made out of one ounce of gold, which has a current market value of about $1,700.
A true collectible can have value beyond just the melt value (for coins, the "numismatic" value). Since you said it's in "perfect uncirculated condition", I'm assuming it should have value higher than just the melt value of the gold. Is that just your description of the condition, or was it graded by an independent grader, and sealed in a case?
When it comes to collectible coins, there can be several factors that effect the numismatic value beyond just the condition - the year it was struck and which mint struck it (identified by the mint mark on the coin) are two additional common ones.
However, remember that there will be a 'value' price (what you would pay a dealer to buy it), and a 'resale' price (what the dealer will give you for it). There can also be other factors effecting the price the dealer offers you - if they already have 5 gold eagles in their vault, they'll offer you less for it simply because they don't need another one that badly. Conversely, if they know a client that is looking for one, or they don't have any and would want to add to their inventory, they'll offer you more. So be sure you get prices from several local coin dealers (often also high-end jewelrs that sometimes sell rare/collectible coins).
There are coin price guides to give you estimates of your coin, so do a little internet searching to see what your particular coin for the year and condition would fetch and compare that to what the local dealers would offer.
You could look at out of town places - but by the time you insure and FedEx your coin to them, the added costs would likely make a local dealer just about as competitive.