Hi Bob,
I grew up in Richmond and am finishing a Masters at VCU now.
Richmond has lots of great places to live right around the campus. The nicest is the Fan, just west of campus between Grace and Cary streets. You can easily walk or bike to everything you need there. Lots of great restaurants, corner shops, small neighborhood parks, etc. There are a few areas on the fringes of the Fan that are a bit sketchy, but the vast majority is great. It can be a somewhat difficult to find a place to live that's really nice at a reasonable price. There are lots of scruffy places available that have been rented to students for years without being renovated or updated. With a bit of searching though, you can find a great place.
Oregon Hill is another popular area for students. It's located just south of campus. Oregon Hill used to be pretty run down, but there' s been a lot of renovation and some new construction in the past few years. If you can find something good there it is a nice place to live. Parking and large parties can be a problem because the streets are narrow, there are lots of students, and the neighborhood is pretty dense. The neighborhood website is oregonhill.net One of the great things about Oregon hill is that it is right by the James River and has good access to Belle Isle and the other parks in that area.
West of the Fan is an area called the Museum District. It' s similar to the Fan, but the apartments are smaller and can be a little more affordable. You'd probably want to ride the bus or bike to campus from there, it has a great shopping district called Carytown that is very convenient. Lots of great shops, restaurants, and grocery stores. Also good access to the major parks and museums in the area. Maymont Park is a great place to spend an afternoon.
Craigslist is a pretty good source for finding apartments, as are Style Weekly (free local mag.) and the Richmond Times Dispatch (local newspaper). Many places don't seem to be advertised though, and it' s worthwhile to come to town, take a walk or drive around the neighborhoods, and look for the "for rent" signs.
In any case, there's great variety in the VCU area and I'm sure you'll find something you'll like. Good luck.