Best place to find airline tickets from LA to Budapest?
There is no best place. The price will be the same for the same flight no matter where you look. It's best to book directly with the airline, but you can use a site like kayak.com to compare your options.
The prices will be the same, no matter what site you use. Sites like Kayak.com and Orbitz.com can let you see how the prices vary depending on the season, the day of the week and the time of the day. If you put in that your dates are flexibly, they will show you the best times to go.