I used to do sound testing in commercial buildings, it was my experience that it is far easier to reduce the high frequency noises than the low frequency. In laymens terms if the noisy neighbors are playing music with alot of bass you may have trouble reducing the sound infiltration in to your dwelling.
The suggestion of hanging curtains is excellent idea for higher frequencies, the lower frequencies require more mass, like adding layers of drywall or concrete walls.
Another cheap idea is bubble wrap applied to the window, just wet down the window and the bubble wrap will stick to the glass, however this makes it difficult to see out.
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