Europe is cheap, during the fall season. Tourists and school crowds are lesser and several destinations are brilliant. Taking advantage of this I would recommend you to visit the countries which normally get very crowded such as Greece, Italy and Switzerland! Perfect weather conditions (yes occasional rain) but total enjoyment of the place and to live with locals and get a taste of the European lifestyle ;) I am headed to Italy probably end of October/early November :)
You can find some budgeted travel destinations in the eastern part of Europe. You can plan to travel to countries like Palma (Majorca), Munich (Germany), Nice (France) and Athens (Greece). Have a memorable trip!