Almost all apartments in Charlottesville operate with a year-long lease. So that makes it more difficult to find short-term housing. Hotels are expensive--they are best for stays of one week or less. Here are some suggestions to help your search:
First, check this site that lists opportunities for short-term housing: http://charlottesville.craigslist.org be careful to make sure the places are near UVA or at least near a city bus stop.
UVA's International Center provides short term accommodations for internationals. However, they have limited numbers of rooms and this option might be a bit expensive depending on your budget. here's their site: http://www.virginia.edu If you are a grad student or visiting scholar, it would be appropriate for you to write the head of your department (or your immediate advisor) and ask if he/she could put you in touch with other faculty who might be able to help provide a room or offer some recommendations. "Sublease" (the verb form) means that person-A has signed a one-year lease but is not using his/her room or apartment for some giving length of time. As a way to save money, person-A will try to find person-B, who will rent the room/apartment (during the period of time, in which it is not being used). In the areas near UVA, it is most common to find "sublet" (the noun form) opportunities for the summer (when many undergrads are out of town). Sometimes there are opportunities for either the Fall or Spring semester because person-A is out of town for one semester (studying abroad, for example). It is more rare to find a sublet for one month or similar short period of time.