Brookhaven is a nice area about 10 minutes from downtown. There are a couple to subdivisions in the area.
The Pleasant Hill Road/South Pierpont stretch is also nice... there is at least one newish subdivision and many other homes along the drive. Very nice rolling hills.
Prairie Village is also a nice neighborhood. Prairie Village is more central to much of Morgantown... within 2 minutes of city limits. Ashworth place is right down the road from Prairie Village, perhaps a little more expensive, and I am not as familiar with this neighborhood.
(I am fairly certain all of the above places are outside of city limits, which can be nice)
South Park has a lot of older homes... some very nice.... many with a unique, historical feel. (Also many are probably un/poorly insulated!). If you go further to one edge of South Park (Greenmont, I believe), you get into more student housing. Also, South Park is in city limits and borders one of the two major high schools.
Also, you might want to consider the South Hills area, which is close to South Park, but a bit more private and houses are generally not quite as cramped together.
There are many nice houses in first ward (also within city limits), that are generally much more affordable than South Park. Elysian Ave, Madigan Ave, Callen Ave, West Virginia Ave, all have some nice homes, and are very close to downtown (but separate enough, generally), and surround a nice park (Jack Roberts Park).
I have lived in the Morgantown area all my life (~26 years) and love the area very much!
A main complaint, however, is that while the University has done a TON for the town, there is a lot of traffic, crazy parties, and crazy nightlife during the main semesters when the majority of the students are in town.
If you do not want to be near the party atmosphere, there are tons of locations to choose from that are still close to town, and also several to avoid!
Let me know if you want any more info.... there is too much to put on one post!