MediaMarkt is a good bet for finding power converters in Budapest. They have them in most malls (Mammut, WestEnd, Árkád, Aréna Plaza, etc.) and you can also order products for delivery online.
For example, here is a 230V/110v AC to AC adapter that allows you to plug in a 110v device with a U.S./Mexico-style plug into a European outlet.
Thank you for the question, Amir! I hope this helps.
I would like to bring my flat iron and curling iron with me to study abroad in Budapest. They are not dual voltage and I bought a converter, but I keep seeing stories of people still frying their hair dryers and such even with converters. Has this been a problem for anyone? Would it be a good idea to leave my stuff at home and just buy cheap ones there?
You might consider just buying new ones in Budapest. Converters do work, but in my experience, your devices may not run exactly like they used to. We have a set of 110v hair clippers that we use with a converter, but the clippers run faster than normal and rattle like crazy. 🙂