Island Quarter

Is a 2001 New York State Quarter minted in San francisco worth anything?
Or a Rhode Island or NC?
If they were minted in San Francisco, then they are proof coins, minted especially for sale to collectors. The minted them in two compositions–the “clad” composition that is the same as normal circulation quarters, and in 90% silver which is what quarters used to be made from before 1965. Probably the easiest way to tell the difference it to look at the edge–the clad coins will have the copper core visible on the edge.
If you found them in circulation, clad proof quarters are really just worth face value, although finding these “impaired proofs” is kind of interesting–I’ve put together a couple of “impaired proof” sets from coins I’ve gotten in change.
A silver proof that you find in change is going to be worth it’s silver value of about $5.
If you didn’t get them in change, then my first bit of advice is to only handle the coin by the edge, and then do it as little as possible. The surfaces on proof coins are very delicate, and it’s amazing easy to put a fingerprint or a “scuff” on the coin, and kill the value.
If you were looking to sell to a dealer, you might expect the following for the clad proofs:
NY: $5.50
RI: $5.50
NC: $5.50
For the silver proofs:
NY: $12
RI: $6
NC: $11
Those are just “ballpark” estimates–a dealer might legitimately offer you more, or less, depending on circumstances.
US Virgin Islands Quarter Release Ceremony