Ed,
If you are going to be affiliated with Dook (correct spelling if you went to Carolina
) then that will be your most affordable option for a lot of golf without 5 hour rounds. It's a good golf course if you get a membership of some sort, by as a daily fee it is way over-priced, IMO.
Hope Valley is, without question, the best course in the area, but it is NOT a club looking for transient members. It is the "old money" club in Durham, as it were, and still relatively exclusive. Regardless, be sure to find a way to play it at some point.
I grew up about 4 blocks from Hillandale, and still think of the place as home. Weekend rounds can be endless at times, but on weekdays you can play pretty cheaply and pretty quickly. Hillandale is the essence of public golf in terms of the clientele, but the greens are always in good condition, and it is a lot of fun to play. Don't sell it short.
Finley is very comparable to Dook as a golf course, but will also cost too much as a daily fee, IMO. I like Finley better when I'm home because I like giving money to a guy in a light blue shirt better than to a guy in a dark blue shirt. If you don't have those loyalties, and the price is the same, it is a tossup.
If you are looking to join a club for the three years in the Durham area, Croasdaile might be the best option. George Cobb course that John LaFoy redid a few years ago. I really like the golf course, and it is a pretty convenient location.
There are lots of other options, especially toward Raleigh, that have been mentioned already and can be googled as well. None are great, but none are terrible, and there is decent golf for a decent price in the area.
One course that I haven't seen mentioned yet is The Preserve at Jordan Lake outside Chapel Hill. It is an affordable Davis Love course that has interesting holes despite not being on the best piece of land.
You'll love the area. I grew up there, went to school there, and will retire back there in a very few more years. Enjoy it.