Most colleges and universities offer dorm rooms to rent for next to nothing to non-students during the summer. The price usually includes meals.
Or, if you don’t mind conjugating verbs while on your European vacation, check into an independent language-immersion program. A weeklong stay at a host home with classes can cost the equivalent of a night’s stay at an upscale hotel in the US. Bonus: you’ll get smarter on vacation! Now, who can make that claim?!