Spent six years in Richmond, so can comment on the city.
Richmond is a divided city, with 5 interesting neighborhoods on the GRTC routes (local bus service).
West End, 10-15 minutes drive from VCU, is a wealthier neighborhood with large houses and boutique shopping along Cary Street (one of 2 main arteries into town). Malls and suburban sprawl mesh into the side of Richmond here. This area runs from the west side of Richmond to the intersection with Boulevard, and from the river up to Broad Street. Groceries stores, including supermarkets, are available.
Slightly farther in the museum district, which is the fashionable place to live. The area starts at Boulevard and continues down into the VCU area, which means this area is normally within biking distance of campus (though there's a wicked hill). Bounded South by the James River and north by Monument Avenue. Mostly old townhomes, but a few apartment complexes. Some local markets, but no supermarkets.
VCU/The fan is from 1st street down to where oldtown starts (about 10th street). There are lots of VCU owned apartments, and cheap eats. Easily the easiest place to live without a car. No supermarkets, but lots of small shops offer competition. Bounded by Broad and the James
From 10th to ~20th is the shockhoe slip, which is the old harbor district. The real downtown, so it's expensive, but the old tobacco buildings have been turned into really nice loft apartments. Farmer's market but no real grocery. Bounded by the James and Franklin Street (where VCU's medical center is located).
Further over, and away from the river, is Church Hill. It's an accordion neighborhood just entering a nice era again. Houses are cheap, but some areas are not very nice at all. Ask a local pizza place if they deliver before you decide to move in (no joke; they won't deliver to the worst places). Some areas are really nice; locals have opened awesome restaurants and cafes on broad street, with some really nice houses and neighborhoods cropping up alongside of them. If you were looking to buy I'd do it here or in the museum district.
I'd detail the other side of the river, but I'd really just stay away.
Some other notes:
1. You probably want a car, pub. transport is no good and it's kinda hilly for bikes.
2. Central VA has some good microbreweries.
3. West end richmond can earn you $35 to 40 a month tutoring.
4. Schools are bad in the city but good pretty much anywhere outside the city limits (if you have a family)
5.Shopping mostly happens towards the west end (there are several open-air malls that are really popular in the summer, with organic markets next to them).
6. The mid-atlantic, inc. Richmond, is very hot and humid in the summer.
7. Decent beach and skiing are both ~2 hrs away.
let me know if you have any other questions, or pm if you want to know something about a particular address.