Where should I sell the Exquisite Sapphire?

I think the best place to start is to get your Speech at 100. There are many ways of doing this from the wiki

1. Selling valuable items. I recommend you need Enchanting, Smithing, and Alchemy at 100 with all the perks and equip items that allow armor and potions to be stronger. This will allow you to make better valued items. Enchant apparel with 2 valuable enchantments, banish and paralysis. Then improve them, but only if it's armor. For potions, make a potion out of 3 ingredients. Then sell them to merchant. Now it's okay if they don't have enough money. The only thing you want to sell for money is the sapphire.

2. Ungrien Glitch. You must be before Patch 1.9 to do this. Talk to Ungrien in the Black Briar Meadery in Riften, ask about Maven, and use the persuade option. If he says he told the truth, bribe him until your Speech is at 25. You can do this again.

Now that's covered, you should spend on 2 perks:

• Investor, 80. Allows you to invest 500 gold. Before 1.9, investing in the Riverwood Trader adds 10,000 gold, making Lucan the richest merchant to sell the sapphire.

• Master Trader, 100. Merchants have an additional 1000 gold.

Now sell them to the fences in the Thieves' Guild [Or use Lucan before 1.9]. You must join them, complete the questline and the jobs so they will have 6000 gold.