The best way to get rid of items that are extremely valuable is to wait to sell them until you want to buy something, or to buy items it never hurts to have more of (say, Ebony Ingots) before selling it.
In the speech skill tree Investor and Master Trader will increase the amount of money. If you invest in a merchant that will increase the gold that they have available by 500, and Master Trader increases all Merchant's gold by 1000.
Also if you go the Thieves Guild route, as you improve the Guild, fences will have more money for you to work with too.
You can also, buy items or training from a merchant to raise their current gold high enough to sell said item unlike Investor or Master Trader that let you add permanent cash to the store this is only a quick fix however the Merchant perk will let you do
this at any merchant that is a trainer or simply has something you want to buy. In general the speech tree will turn all of Skyrim into the Thieves Guild if you invest enough perks.
In addition, the best way to sell quick is to use the Wait feature. After a few days all their monies is replenished so you can sell them some more and not have to travel and go through loading screens.
Riverwood trader has the most money (may need to remove latest update), but also Whiterun is pretty good with Warmaiden's having two sellers (Adrianne outside & Ulberth inside)
The Riverwood Trader (the guy you retrieved the claw for in the early game) will have just under $12000 each time you visit, provided that your speech skill was high enough for you to invest in him. That's the most money from a merchant that I've seen so
You can also do what Sunmaker suggested and increase your Speech skill.
I like to make a super barter potion, give a gold to the beggar, wear a Zenithar amulet and get a blessing from zenithar, then when I'm armed for bear i go make Belethor and the nasty ladies at Radiant Raiment pay the maximum amount they will pay and clean
out their tills. It doesn't matter what I sell, I just like sticking it to them because they are mean. Warmaiden's is the best place to sell just because there are to buyers with a lot of gold. never found getting gold to be a problem actually. If need some
I go sell some of the massive amounts of stuff that costs more than anyone has anyway that I have stashed in all my houses.