Matthew,
I don't live in Richmond but am there for business 2 or 3 times a year. I'm sure some of the locals can give you some more info.
But from what I've seen and heard, Kinloch is the cream of the crop. I've never played it, but it is almost universally praised on here. I know Country Club of Virginia (2 courses I think) has a Flynn pedigree but apparently has been altered quite a bit.
On the public side, I think your best bet is to hop on I-64 and head towards Williamsburg. Royal New Kent is not too far from Richmond, and then as you get to Williamsburg there are lots of options. Golden Horseshoe gets lots of kudos. Kingsmill has 3 or 4 courses. I played the course by C Strange (Woodlands??) and it was an ok resort course. Played the River Course by Dye and the staff treated me like crap so that probably altered my view of the course.
In Richmond, Providence is a Lester George that is inexpensive and a fun course. Belmont is a Tillinghast course owned by the city which if renovated could be great, but is usually in pretty rough shape. Federal Club is a Palmer that just went public..I wasn't too impressed by it. Hunting Hawk is east of Richmond off I-64 that I liked my one time around, but played w/some non golfing types scrambling and dringking.
\Independence is a Fazio public that gestspanned on here, and while I wouldn't call is special, it is worth a play every now and then.
Where are you going to grad school?