Such variables are generally best found via the guess and check strategy.
Implement your game logic in such a way that is refresh agnostic (Say for instance, exposing the ms/update as a variable, and using it in any calculations), then play around with the refresh until it works, and then keep it there.
As a short term solution, if you want an even update rate but don't care about the evenness of the updates per second, 15ms is close to 60 updates/sec. While if you are about both, your closest options is 20ms or 50 updates/sec is probably the closest you are going to get.
In either case, I would simply treat time as a double (Or a long with high-resolution), and provide the rate to your game as a variable, rather then hard coding them.