Bull Island is man-made - well, formed as the result of sand building up against the (man-made) harbour wall. A stunning long sandy beach with an important bird sanctuary at one end, and a quaint wooden bridge, harbour wall, and monument at the other. If you aim for the middle section, you'll avoid the boy racers (they're not intimidating - just a bit annoying). On a windy day you'll have some impressive kitesurfing to watch, too.
Look out for the Bull Island if you come in on the plane. The northern approach often takes you directly overhead.
Bus routes 103, 104 and 130 run next to Bull Island (ask the driver), or Clontarf Rd DART (suburban rail) station followed by a 20 minute walk along the sea wall
Maybe it's all too, erm, "literary," but the trip down to Sandycove on the DART is a must. You can dive into the water at the legendary Forty Foot though, since women are now allowed at this gentlemen's bathing spot you need to keep those togs on. And right above you is the Martello Tower where Ulysses begins, preserved as a slightly overpriced but totally entertaining little museum. The ability to stand atop that stone tower, as Stephen did that long ago Dublin morning and look out on the bay is a wonderful thing for those who love Joyce's work.
Take the DART south from Dublin to Sandycove, walk down Adelaide Road to the water, turn right (east) and follow the shore to the Forty Foot (at Sandycove Point)
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