St. Anne's park is an big old demense left to the city by one of the Guinness families. The old house burned down decades ago and the central avenue now leads to a small raised site. The "front garden" of the house is mostly lawns, now used as football pitches. there's also tennis courts and a mini-golf. The "back garden" is woodland down to the coast - you can then walk out to the Bull Island (formed by longshore drift after the building of the harbour wall) which has an amazing beach.
The park, easily accessible by DART (suburban rail) and bus 123 has a phenomenal rose garden which is at its peak in June/July.
St. Anne's Park is another lovely park in Dublin. It is not the size of Phoenix Park but also not as crowded. One of the few places where Red Squirrels can be seen relatively easy. For a nice stroll where you can enjoy beautiful trees, birds and the scarcer of the two Squirrel species, St. Anne's is ideal.