I have several boxes of comic books from the 80's nothing worth paying off my house or anything, but I do have some that maybe worth in the hundreds.

What's the best way to sell them off?

I'm in the same situation. Someone who owned a comic book shop owned me money. I got multiple cases of books instead.

Most of the folks I know who have gone into comic book shops of late didn't do very well at selling large amounts. (Obviously depends entirely on the store). Seems most have had more success at using Amazon and Ebay. I've sold some 1st edition books on Amazon pretty painlessly.

Some of the 80's comics might be worth holding on to a bit longer. I have runs of Indiana Jones, Johnny Quest, Vampirella, and others that I will likely keep and see what happens. You likely know comics better than I do, but before selling I would take a look at current auctions and Overstreet.

Some of the ones that were considered trash in the 80's have bumped up quite nicely in value, particularly if you have a run.

I had six long boxes, and whittled it down to two short boxes of core books actually worth some coin.

If you actually want to make maximum dollars, you're going to list individual books or series and sell them yourself. If you just want to dump, you'll take a bath. Not unlike selling a gun to a gunshop or say, on Gunbroker.

It all depends on exactly what you have.

Frankly, except for very specific things, the 80's and 90's are dead zone. Ask me how I know.

When I "culled" mine, I went through and made a detailed list, with condition, and then did the legwork for maximum dollars.

Most comic shops are neck deep and will only pay for the rarities.

Comics haven't quite come back yet, even with the popularity of the Marvel movies.

I'm sitting on some real gems at this point, and some worthless comics that I like.

Taking the time to sell individual books is the only way to see real money, but it costs time.

If you're looking for maximum profit, you'll have to have your comics graded individually by the CGC. It's an expensive service but it guarantees that there is no ambiguity with regard to the value of your comics.

If you don't really care to go that route the next best way to sell comics is to sell them yourself at a comic book show or convention. You'll have to price them yourself which requires researching each comic individually, spending the money to rent a table at a show, and the effort of sitting around chatting with people and haggling over prices.
--Additionally, you could put in the effort of posting your comics on eBay or Amazon.

If you really just don't care and want to just unload your comics the final choice is to sell to a comic book store. This will net you the lowest price possible for your comics. You'd be extremely lucky to get $20 for a $100 comic. A comic book store will only buy the most valuable or rare comics in your collection. The rest will be rejected outright and you'll be forced to either offer to sell it in bulk for pennies on the dollar or take it and sell them through other means (see option 2).

You could try looking into donating to a library (public or school) or to Goodwill, as an absolute last resort.

I'm currently stuck with over 3,000 comics in 12 long boxes. There's value in there but I'm too lazy to try to sell any of it.

Unless you have first appearances of popular characters or something really rare or special, most comics from the 80's and 90's aren't worth much at all. If you have any that are worth several hundred dollars I'd have them graded and put them on ebay. You'd probably find you're largest market there.
Grading them increases their value and gives you some protection. I sold a comic on eBay several years ago and got burned. I went into extreme detail about the comics condition, listing all of its flaws. The buyer claimed it had a flaw that I didn't mention so he wanted a refund. I clearly stated that there were no refunds but ebay's policy is to side with the buyer. I refused to give the refund because the flaw the buyer mentioned was not there when it was shipped.
I was banned from selling but I got the comic back. Sadly, it lost a lot of its value because of the damage the buyer inflicted on it. Just giving you a cautionary tale of risk where returns are involved.