I buy and sell old coins and bills, and what i would do and what works for you might be very different so i'll just go through some of the options and let you decide what works best in your shoes. There are 2 ways to sell a collection, you need to decide if you want to sell it as a whole, or if you have the time and interest, to part it out for (potentially) more profit. I say potentially because it could be the case that it goes for more as a collection, though that is very rare, and usually it parts out for much more when it comes to coins. If you decide to sell as a whole, MAKE SURE YOU GET MULTIPLE OFFERS. I can't stress that enough, if a shop or a buyer is going to make you an offer, make sure they know that you will only be selling after getting multiple offers as well, this may very well increase what they were about to offer you. Even if an offer seems out-of-this-world-crazy-high get a second, third or more opinion before selling.
You can sell as a whole to coin, antique or pawn shops, or to independent coin resellers like me, though we all pay somewhere between 50-90% of retail value for a collection (or less if they aren't very honest). I try to pay around 80% of what i expect a collection to sell for because it leaves me more than enough room with the very low expenses i have, and is high enough value to beat pretty much every other offer someone would get in my area. You could also sell a collection as a whole through an auction house, who would likely sell it in smaller lots for you. Is your collection mostly loose coins or are they mostly sets and well organized? I find a well organized collection (each coin in a coin holder and labeled, coins in mint sets etc) sells MUCH better at auction than bags or boxes of loose coins. So i would advise you put some effort into the presentation if you went the auction route. The auction house would likely take a large commission, however they may be willing to negotiate a lower commission on a sizeable/valuable collection. I sell some coins and a lot of older bank notes through my local auction house, here are some things i've noticed. What things sell for can vary wildly from week to week depending on who is there, so an auction house that would be willing to sell a collection over a series of auction nights may help average out what you get rather than risking everything selling on a "cheap night". For coins or bills $1 or more, my auction house only charges me commission on the amount it sells for OVER face value. i.e. If i sell an old $100 bill at auction, and it goes for $125, i only pay commission on the $25 above the bill value, this is especially important for selling larger denomination currency. Ask you local auction house if they would do that for you if you sell through them. It may also be worth going to an auction night when they have some coins up for auction and see what kind of interest the bidders have in them before going this route, or selling a small portion of the collection through them first to see what kind of money it brings in. Ask multiple auction houses if possible what they can do for you as far as commission on the collection.
If you part out a collection yourself, you would need to research what you have and what to look for to value it. Once you have a good idea whats what, you can post each coin or small lots of similar coins for sale online. I'm not sure what your best choice is in your area for this, but i like the local Facebook buy and sell groups for this kind of thing in my area over craigslist type listings for low-medium value coins and sets. I wouldn't post anything on craigslist/facebook worth $1k or more as this may attract attention from the wrong people, and instead would go with an online auction (eBay or a coin or collectable specific auction), or sell to a coin shop (get multiple offers!) for this kind of item. Don't be afraid to call up coin shops in other cities and see if they would let you email them photos of coin/s and see what they would offer you if you suspect they may be worth a lot. The only problem with going through and learning about each coin (other than how time consuming it is) is that you might start finding coins interesting and end up keeping the collection out of interest in them, haha.