Does anyone know how much a 1964 Singer Sewing Machine, in mint condition, is worth?

Have a look at what their going for on eBay

I agree, eBay would definitely be one place that you could try.

Another thing would be to perform a Google search for machines like the one that you have. Below, is a link for such a search.

1964 Singer Sewing Machine for Sale - Google Search

It would be helpful to include the model number and/or name to the search in order to narrow things down a bit.

There is a 1964 600 Singer Sewing Machine that can be found via clicking on the following link that's being sold for $150.00.

1964 SINGER 600 SEWING MACHINE