Unfortunately, this happens to be the case for many apartment complexes who offer 1-year leases and then allow renters to find someone to sublet their room for summer. What most people do in this situation is either find a friend's place they can crash at until classes end or stay at a hotel.
An option are Craigslist ads that offer short-term stays. Another option is AirBnb which allows you to live with people on a daily, weekly or monthly basis.
Staying at a friend's would be the most economical option when compared with staying at a hotel in the area that can range from $45/night to $70/night.
If you have another roommate that can split the cost of a hotel for a week with you, it ends up not being too expensive. These hotels come with TVs, cable, high-speed internet access and even some appliances.
Here are a few hotel choices with decent rates for a college student's budget that are all five miles or less from UF's campus:
Quality Inn University- http://www.qualityinn.com/hotel-gainesville-florida-FL4432.0 miles from campusRates starting at $69/night
Extended Stay America- http://www.extendedstayamerica.com/property/Extended-Stay-America-Gainesville-I-75-hotel.html2.2 miles from campusRates starting at $55/night
Budget Inn- http://www.budgetinngainesvillefl.com/4.1 miles from campusRates starting at $45/night