This picture should help you figure it out a bit better.
in the above picture MCV is located right above where the purple line intersects the O of downtown
Sketch areas that you probably don't want to live in include: oregon hill, Jackson ward, Randolph or anything with court in it (ie Gilpin court). Also, dont live right across the river from downtown (ie called manchester on the second picture). Finally dont live too far north of broad street in church hill. For those of you that went to the financial aid workshop the director lady told you that Jackson ward is a good area to live in. I pretty much crapped myself when she told you that. Jackson ward is a really sketchy, really dangerous part of Richmond. Don't live there.
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Here is a second picture that shows things a bit further east
Here MCV is located right around where it says "court end"
The Fan:
http://en.wikipedia.org/wiki/Fan_District
Note that while Wikipedia doesnt consider west of boulevard 'the fan' many in Richmond do. Others refer to west of boulevard as "the museum district." Either way it is nice to live near carytown (shopping/eating area). You will be good living pretty much anywhere in the fan area. But the further away (west) from the undergrad campus, the quieter things will be. Generally around the 2000 block (of streets parallel w/ broad st) you should be in good shape. Other considerations are that there are a lot of bars on Robinson. So you might want to live around there (i think about 2500 block). The further west you go, generally the safer things get.
Church Hill:
http://en.wikipedia.org/wiki/Church_Hill
Note that you dont want to live very far north of Broad street. If you can, stay SOUTH of broad street (red line going up church hill). Really I cant stress this enough. If you go like 10 blocks north of broad around church hill you will get shot. Only half kidding about this. South of broad street has some very beautiful areas and some very nice apts. North of broad is a great place to buy crack. You see the dark black line going north of church hill, that is where the projects are and is arguably one of the most dangerous area of Richmond. So stay away from it.
Shockoe Bottom:
http://en.wikipedia.org/wiki/Shockoe_Bottom
Apts are spotted throughout here generally above shops or in converted industrial buildings. The apts generally have a lot of character but, it can get loud if you are near the clubs/bars. Most of my class lives in the bottom so that is a consideration, plus it is nice and close to MCV. Basically on a decent day you can walk from the bottom. Things can get pricey here but if you look you can find a cheap place.
Other notables are the west end and the southside. Unless you have kids, these are kinda far. If you have kids: freeman and godwin school districts are good in the west end.
PM me if you have questions.