Visit bookstores in your area or online. Barnes and Noble, Dutton's and Borders have extensive catalogs of books. You will not be able to find the complete set of 200 volumes here, but merely the books post 1987 (the last series in production that's still in print). Only some of the more popular titles of that 127 set of the Hardy Boys may be available. You will pay full retail price at these stores, but it will give you a good jump.
Search for library sales in your area. Every so often libraries replace books that are worn or remove books from their stack that aren't popular. This is a great way to buy books for pennies on the dollar. Check the young adult section to find Hardy Boy Books for sale.
Post a listing on community websites. Rather than searching, let people with collections come to you. Post on community and chat boards describing what you are looking for. Be as specific as possible and offer to pay what you can afford on the books. Sometimes your simple passion will shine through and you may get straight donations.
Check out ebay and other auction sites online. Ebay has created new markets for older items. This will be especially helpful when trying to track down some of the older books in the series, which were published in the 1950s and mid-1920s. A simple ebay search returns hundreds of results.
Procure out of print books sites such as bookfinder.com and abebooks.com. These companies specialize in books that are no longer published. Tell them what you are looking for. If it's not in their stack, they will have roots in the world of hard to find books and be able to point you in the right direction.
Swing by such places as Salvation Army and Goodwill stores. Many times people simply donate large quantities of books after someone's death or if they are moving. There are some great Hardy Boy Books to be found among the contents of these stores.