For the ISAP-program with the GMU Fairfax, VA is a good place to live, because it is close to the university. The experiences of current students will be published here soon.
If you prefer an apartment in Washington, D.C., you have to think about higher prices, commute time and the tense housing market. Also, in some districts (like in every large city in the USA) the crime rate is relatively high. For security reasons, only the northwest of Washington and Arlington are recommendable.
In the past, it was not recommendable to purchase an apartment east of 16th. In recent years, these districts were upgraded, but they are still in big distance to the GMU campus.
Adams Morgan is south of Columbia Heights. This district is recommendable and relatively safe. It is popular with younger people because of its closeness to 18th street. 18th street has many bars, restaurants and pubs. Thus, the apartments and even the rooms are relatively pricey.
West of Adams Morgan, Georgetown is a very beautiful area. It is quieter than and not as varied as Adams Morgan, but there are very nice houses with trimmed front yards and the district is very safe. In the centre of Georgetown, there are also many bars, probably the most interesting part is M-Street. A disadvantage is the big distance to the next Metro station.
Situated north of Georgetown, Glover Park is a beautiful place to live and there are opportunities to get a room in a grouphouse. The Metro-connection, however, is even worse than in Georgetown, therefore it is probably too time-consuming for students of the GMU.
Tenleytown is even more to the north, but the next Metro station is closer. However, you have to change trains to get to the GMU, so the commute time is high. The area is as beautiful as Georgetown.
In the west, Arlington adjoins Washington DC directly and is situated at the Orange Line, so it has a locational advantage for students of the GMU. Behind the high-rise buildings of Rosslyn, North Arlington has a suburban flair. The inhabitants are mostly rich families and the crime rate is very low.
Your decision depends on offers, demands and personal expectations. It is, however, reasonable to get in contact with current exchange students. Maybe there is an opportunity to get there rooms.