Don't give up too quickly. I recently sold off some vinyl and was surprised at how much they brought. I sold 200 records for about $4,000. The big money came from the Mobile Fidelity and Nautilus albums (some still sealed), but I sold $800 of random albums from the 60's and 70's. It's impossible to guess the titles and artists that you inherited but get some advice from a used record store. Records in decent shape from the 60's and 70's may only bring about $4-5 per record, but if you have enough of them it adds up to real money. Good luck!
Selling a record collection is time consuming. As stated above, most old records are only worth a couple of dollars, but some may be quite valuable. The only way to know is to spend the time looking up each and every record on the web to determine its market value. After that, sell or donate the ones with minimal values to a record store or Goodwill and put the few gems up for sale. If it sounds like a lot of work, it is.
Most old champagne 50's...60's music can be found at good will stores dime or quarter per piece. In 60's they become absolutely boring compared to Al Green, Bo Didley, G.Lewis... Pop music always appears for short period of time than goes off the listeners list. I'd say as a living vinyl seller that the best place for selling these most efficient is discogs.com
Obviously, content and condition determine the value of any used records. If you have the Doors or Beatles in good shape, sealed in plastic to protect the covers, they're worth much more than 50 cents. The proof for me was the four guys sitting outside my house for an hour prior to my vinyl garage sale. Each of them bought $100-$200 worth of 60's/70's vinyl, most around $5 each. Again, get some advice from a used record store, or the internet. You might have a treasure.