Active noise-cancelling headphones used to be prohibitively expensive, but in recent years, they've entered more affordable realms. The Jabra Elite 85h in particular has turned out to be the most economical set of these in the over-the-ear headphones market and has been available for $200 over the last few weeks. If that was still above your budget, you might be more comfortable with the new all-time low of $157 on Amazon, which is $143 off the MSRP.
The Jabra Elite 85h can be used both wired and wirelessly thanks to a 3.5mm port and Bluetooth. A built-in microphone allows you to make phone calls with it, and the water resistance will give you peace of mind when you wear the headphones out in the rain. In our review, David Ruddock calls the 85h "winners," and says they often have superior noise-cancelling capabilities than their more expensive counterparts from Bose and Sony.
To get the Jabra Elite 85h on Amazon, head to the link below. Even though they have an unfavorable Assistant integration and are a bit heavier than comparable Sony or Bose products, you can't go wrong with them at the current price.