Overall: The bouldering around Athens does not warrant a standalone visit (at least not for most folks). However, if you are traveling through anyways, perhaps for some live music, drunken revelry, or a friendly visit, you might want to bring your bouldering gear. Serious climbers will find a few gems worthy of their attention, along with a slew of ok problems that have a bit of loose rock or dirt runoff. Check out Athens on Wikipedia.
Season and Rain: The best season is fall, but any time that there has been a dry spell of at least 2 days will work. Very little of the climbing is rainproof and all of the rock is weak and easily damaged when wet. Indoor climbing options are limited to“Ping” the tall but narrow, Entreprise top-rope fest in the student Rec Center. Another similar wall is located at Hocking College.
Concentration of problems: Low to medium. The East State Street area (with COAD and Trailer Park) has the largest collection of established problems within moderate walking distance. Witches is more limited, as are the formations near Dow Lake. The best problems in the area are widely spaced. However, people who are willing to accept some contrivance, are not averse to spending time on easy slabs and traversing, will find several of the areas to have enough to warrant a visit.
COAD / Trailer Park / Boulder Cove / Lions Head / Etc. This area has the highest concentration of worthwhile problems with a single parking spot in Athens. This general area is the best place to start on your visit to Athens.
Witches. Scenic view of Athens from the south east. A nice collection of fun, but sandy problems.
Far East. Highest concentration of difficult problems, though many are short and sandy with some fragile holds; avoid after rain. (sorry I don't have an overview of this section)
Court Street Crag. Bouldering and a couple of routes / top ropes. Great potential for eliminates, mostly solid rock.
There are several additional areas that are less travelled. Grab a topo and go exploring.
Biking angle: In addition to drunken revelry (to make the visit worthwhile) cross-training athletes should bring their MT bikes. Many of the better boulders are accessed via bike friendly trails. A Mountain bike / bouldering biathalon is a great option for getting the most out of your visit. Throw a minimalist pack on your back and start at Sells Park, and do a circuit heading east on the Rockhouse trail, hitting the COAD boulders, then the various stops at Trailer Park. Then either reverse your path or bomb down cucumber tree connecter to the road and return via the pavement. GOOD single track trails (closed when wet).