Where can you locate a reputable appraiser for the 1882 silver dollar coin?

A coin dealer would be about the easiest place to go. There are good coin dealers and bad ones. If they know you are not going to sell the coin to them I think you would have a better chance of getting an honest appraisal. A good idea would be to get a second appraisal but remember that grading coins is strictly a matter of opinion and what one person may see as a coin in one grade, another may not agree so even with 2 appraisals you may have a considerable range of value.