My inventory is full, but with very valuable items. I want to sell them, hence they would give me a lot of coins.
Where do I go to sell them? I went to Whiterun in the General Store, but no option to selling these items.
Help please.

Find a vendor, talk to him, ask what he has for sale, below the white line are your items, which you can then proceed to sell

Wait, vendor as in a General Store or just a regular small vendor selling small items?

Some items have to be sold to a specific type of vendor, or the vender doesn't have the money to buy the items.

When it comes to expensive weapons and armor, try looking for a blacksmith. Scrolls and potions, try magic or alchemist vendor. Alot of Misc stuff, thats usually good to sell to general traders. In the lower right hand corner next to your money in the the buy and sell window is the vendor's money showing how much they can spend on buying your stuff.

Thank you! That's good information to know.
But, when I want to try to sell something to the General Store clerk, it doesn't let me go down to my items at all. Only for what he has for sale.

Its possible you have nothing (s)he wants to buy, or doesn't have the money to buy it. Try vendors in the larger cities, they have more money and a wider buying range.

Your stuff is underneath his. So you'll have Weapons, Equipment, Misc etc and then a dividing line. Under that line is your stuff.

Cities as such in Riften... Solitude, etc?

Yea. I'm guessing you have armor and weapons? Those are usually the things that clog up inventory. WarMaiden's in Whterun I have found will usually buy all weapons and armor.