Looking to exchange SAR with US Dollars

anyone ?

Most US airports have a place to exchange in their international terminals, but there is always a fee.

I think the exchange rate we get from the bank isn't that bad. You may actually find it worth the hassle of getting money exchanged from outside or open market.

I use SABB since I have my salary account there.
Their rate is fixed at 3.753998947 SAR to a dollar

This compared against your target rate (i.e. 3.75010 SAR) results in a loss of only 27 halalas for every 1000 SAR exchanged. This comes out to be just 0.27%.
And you get to do this in an instant, online via internet banking.
Compare it with the hassle of going somewhere or to some individual for exchanging currency.
Also, keep in mind that getting them from open market would always have the risk of a fraud, where as with the bank, it is highly unlikely that bank will give you fake currency notes.

A while back I might have taken you up on the offer, being without a bank account and therefore unable to exchange my dollars for riyals.

I think I eventually got 3.75 at the bank.

I agree using a bank is much less fraught with risk.