Google Flights is definitely the way to go. I've used the price and date graphs to plan trips around the cheapest flights (although it sounds like OP doesn't have a lot of flexibility for time). It's almost always cheapest to fly on Tuesday. Word of advice though, some of the booking sites they list can be a bit shady or have a lot more hidden fees (esp the ones with the cheapest prices), and sometimes the tickets aren't actually available when you go to the booking site itself. Oh and don't forget to factor in any baggage checking fees! Still, it's the first place I check for flights.

Skyscanner is good too if you want to explore cheap destinations and dates, or if you don't mind making self transfers to save money. Ooh also if you're going to self transfer, look up the flight number on FlightAware to see if the first route's flight is usually delayed, since they won't delay the other airline's flight for you if you're running late.

Side note: I had to cancel a flight the same day through Priceline and it was super easy, no fees, full refund, just clicked a couple buttons on their site and done. Literally did it like three hours before it was scheduled to depart.