Well I live din Budapest for 3 years and even after leaving, I still went back for the 3 follwoing years so I know that amazing city pretty well. i think you should try and get there if you can…but it would be a big shame to stay for just such a short period of time…hungary is sooo beautiful…there were not many turists when i lived there, but you should also get away from Budapest and see just how beautiful the rest of Hungary is…go to Esztergom, Eger, Lake Balaton, and many small nice towns.
Good luck and have fun.Dont forget to try the amazing ice cream in Budapest…so many wonderful flavours…and also the marizpan in Szentendre too:)