I have a discover card, American express, HSBC visa card, National city bank Visa.

I prefer to close two of them and stick with two. Which are recommended to close ?
Also, does closing credit account hurt my credit score ?

I would keep the AMEX and one of the others which has the lowest interest rate.

From a credit report standpoint, the two you close will show you closed them, not the issuer. If you are not deeply in debt, it could be seen that you were taking proactive measures to control your own financial situation.

If you carry a balance, the lowest interest rate should be your first choice.

Then consider cards which have a cash back program. Discover has this feature, I don't know about the others.

Then keep the cards which you have had the longest. When someone views your credit report, the longer you have had an account will improve your creditworthiness.