This started when I decided "Hey, I'll try go to Farran Woods this weekend".
Dear reader, I don't own a car. I did not make it to Farran Woods. Google Maps was unable to plot a route, so I went and started working one out by hand, finding it difficult enough, but eventually spotting that a pretty hefty chunk of Cork is not really served by public transport.
Farran Forest Park is a forest park, owned and operated by Coillte, the state forestry company (who really deserve their own post sometime). It is one of a whole bunch of forest recreation areas Coillte own and operate.
The closest bus stops are Farran (3.5km), and Coachford (4.5km) away.
Farran is served only by the bus number 233, which seemingly runs only a handful of times per day, sometimes not stopping in Farran according to the timetable (direct linking isn't working on the Bus Eireann website, go look it up yourself). Coachford is in the same boat - being only served by the 233.
Now, assuming you make it on the bus out to there, a 3.5km walk isn't bad if you are able bodied and all that. There is still the risk of getting stuck, given the area is only served by one bus.
So lets find another forest recreation area in Cork. I decided on Warrencourt, which you can get to from Kilmurry by a 2.3km or so walk. However, Kilmurry is again only served by the bus number 233. It does also have a local museum about the War of Independence though, so I'll have to venture out there sometime. It is also close to the spot where Michael Collins was assassinated by anti treaty forces during our Civil War.
Mullinhassig Forest Park suffers the same fate - nearest bus stop appears to be Coachford.
I think you are seeing a theme here - there are pretty large areas of Cork, full of stuff like parks and national heritage, that are basically only served by a scant handful of buses - a car is really necessary for getting around them. I seem to have found just one of them.
You could, in theory, cycle the area, but I'd recommend taking out a hefty life insurance policy and making me the beneficiary first.