Skyscanner is one of the best sites for comparing flight times and prices. It searches a lot of different airlines and that includes many budget carriers. Be careful as some airlines opt out, Southwest Airlines for instance aren’t listed. The company also offers open jaw flights.
Google is obviously going to be an excellent option to start searching for flights. Google Flights has a map function that lets you see flights all over the world. You can see where the cheapest destinations are and which dates.
Momondo is a great website for finding the best deals and like skyscanner their calendar view lets you see which days are cheapest to fly on. They are very good at searching on sites other companies don’t. This is a great site to start on. The site also offers open jaw flights.