What is the value of an 1890 Wyoming quarter?

It's not from 1890 and it's not from Wyoming.

If you look more closely at your quarter (you did wonder how a 120 year old quarter could look so shiny, right?) you'll see it has 2 dates. It's a modern state quarter. 1890 is the date Wyoming was admitted to the union. The other date is the year it was minted.