As of 2015, a good place to evaluate a Morgan dollar coin is the Coin Study website. The site also offers tools for evaluating other types of coins.
Older Morgan silver dollar coins are created with 3/4 silver. Coin Study grades coins based upon the mint marks and the coin's condition. Coins are graded with uncirculated, extremely fine, fine and good conditions.
Another good place to have Morgan coins appraised is PCGS. The site offers more than 292,000 current coin values as well as historic coin prices. Coin appraisals are available for Morgan coins that were made between the years of 1878 and 1921.