Check to see if there is a refiner in your area. A refiner will probably be willing to purchase your silver. Many gold refiners also buy silver and other precious metals so check them out. Search the phone book under refiners, gold refiners, silver refiners or other similar keywords. Refiners can generally pay you more than a pawn shop and can give you instant cash.
Sell your silver on eBay. Silver sells well on eBay. Do a search on eBay and check going rates, many times you can get just as much or more than selling to a refiner but it could also go for less depending on auction close price.
Sell your silver to a pawn shop. They may not give you a very good price compared to other places but you can get quick cash. Check your phone book to find them in your area and call them to check on prices and what they buy.
Sell your silver to a buyer by mail. There are many businesses advertising online and off that they purchase gold by mail, many will also buy silver. Do a google search and there will be many to choose from. Two that I would suggest are gold kit and cash4gold. They both also buy silver as well as gold. They also may not give as good a price as a local refiner but it might be worth a try.
You can also sell silver bullion at kitco. They even pay the shipping. Check their website for details.