Columbia's most popular course is Earlewood Park, near downtown. It is a rather short but very fun course, owing to huge hills and trees, to the point it is favored by some top pros....and beginners.
Columbia's other course is Owens Field. It is much tougher, with both boomer holes (600'+) and very tight wooded holes. It is a course some love and some despise; you owe it to yourself to check it out to see how it suits your style.
Crooked Creek, in Chapin, is about 25 miles from downtown. It is a very fine wooded course. Note that it has 18 holes with dual teepads, relatively short but interesting. It also has an additional 8 holes that start, more or less, after hole 1 and come back in near the tees of holes 6 or 13.....so you can't just tack these on to your round. They are longer and more challenging than the standard 18. They also require a guide, so once you've played the 18-holer you should track down someone to show you these holes.
League play in the area currently consists of
* Wednesday night, random draw doubles at Earlewood, average attendance of about 20.
* Thursday night, randam draw doubles at Owens Field. Average attendance much lower (less than 10 I think, though I've not been there).
* Saturday morning, various formats at Crooked Creek.
If you venture to about 40 miles there are good courses in Orangeburg and, depending on your skill level and definitions of a good courses, Newberry.