What is the date of the most valuable US quarter dollar?
That's an extremely broad question. Quarters have been issued since the 1790s so there are many valuable issues, and the "most valuable" title can shift as time passes. Some of the highest-value quarters are 1796, 1870-CC, and 1871-CC. You can find a full set of current prices at any number of web sites. One good portal site is http://www.coinclub.com/prices/
By far, the most valuable quarter is the 1916 Standing Liberty Quarter Dollar - its value in good condition (G4) is: $3000. places the value of the 1916 Quarter at $3900 in G4 and $35,000 in MS66 (but look fast, it may be higher by the time I finish typing this). The first US quarter from 1796 is listed at $12,000 and $400,000 in those grades.
Quarters have been issued since the 1790s so there are many years and mint marks that are valuable. You can get an overview from a site such as http://www.coinclub.com/prices/ At least within the last hundred or so years, two of the most valuable quarters are a 1901-S Barber quarter and a 1916 Standing Liberty quarter.
One Dollar bills with low serial numbers, such as 00000001 to 00000100, are sought after and can sell for up to $2,500 in mint, uncirculated condition. The most valuable One Dollar bill to date is the Rainbow Note, which was produced in 1869. It features a portrait of George Washington and a scene of Christopher Columbus discovering America. It is called a Rainbow Note because it was printed using multiple colors. The Rainbow Note One…