The East centres on Dublin a capital city that has few equals in accessibility to good walking. You can see the hills from the City Street, and a bus ride will take you to the start of half-a-dozen walks that will keep you happy for an hour or two. Further away but still easily accessible for a day's walk are the Wicklow Mountains, a 100 kilometre long rounded ridge of granite into which the Ice Age carved some beautiful valleys of which Luggala and Glendalough are the finest.
There are many circular walks to be made in these mountains, with access from the good roads, which edge them both to the east and west, which are well-served with buses. The walking is generally easy, though there are boggy sections to be crossed. The main ridge makes a fine long day's walk over a series of rounded summits. On a clear day you can see Snowdon Mountain in Wales. Because they are close to Dublin, you will find plenty of walkers out on these hills at weekends, but if you want solitude you can find it during the week.
The Wicklow Way starts in Marlay Park a short bus ride from Dublin city centre and works its way down the east side of the mountains, looking into the best of the valleys as it goes south through woods, over rough pasture and along lanes, the first section of a Waymarked Way that you can follow all the way to Kerry.