Soundproofing a room cost effectively
Before you replace the windows, you may want to try sound dampening drapes. Google search and a few companies will offer solutions for home theaters and other rooms.

I have single pane windows in my house. In the winter I install a second, plexiglass insert to help with heating costs. But it does make a huge difference with noise. If you want to experiment, get some scrap plastic or plywood and cover your window. It will look terrible but at least you'll get a feel for how it would be.