[swarmee]

You need to define "fair." Is it 20% of the raw value of an ungraded collection, or 40%, or 60%, or 80%? There are vendors here on the board (like Sean Bassik's Invest In Baseball) or JustCollect that will make you an offer on your entire collection.
If your cards are sorted and in investor grade, you should have no problem selling them. But your version of fair and a dealer's version of fair may not be the same. If you want to make the most out of your collection, you'll have to put some money down to grade your stars. Why sell your Mantles raw for $200 each when they could be worth thousands if they pull NM-MT PSA 8s?
Taking it to the National and shopping the whole collection (or just parts to each dealer) sounds like a great idea, but you need to be realistic with eBay pricing, not book value. If you're not willing to take the time parting out your collection, that's what the dealers you'd be selling to would have to do, so you'd have to be willing to let them have their profit margin.
So do your research. Call some of them before the National to get a feel for what they'd offer in person for a collection like yours.
The more work you put into it, the more you'll get for your collection. The shortcut is to sell it for much less than it's worth to get rid of it.