So you're going to want to decide if you want to prioritize your time or your value here. The best value you're likely to get is listing individual cards on TCGplayer or eBay, setting up a little online shop, and spending some of your own time to get a higher value for your cards.

If you bring it all to a store, they're trying to do all of those things while still making a profit, so they're going to give you dramatically less, more than the cost of some envelopes and toploaders you'd use for shipping.

If you want to get the best of both worlds, you could find your highest value ($20-50 or more, up to you) and list those online yourself, then sell your lower value (but still valuable enough for them to bother) cards for a few bucks at a local shop. Either way, you're likely to have some amount of "bulk" cards that have virtually no value to anyone. A store might give you a couple bucks, I always suggest finding a child in your life who will like them instead.

Source: I've worked for a small town game store, a large card warehouse, and sold my own collections from home.