It's a 3 hour train ride from Dublin to Galway. If you want to see part of Western Ireland, you could base in Galway and easily take day trips to places like Cliffs of Moher, Aran Islands, the Burren, Connemara to get your nature fix. Many tour operators run out of Galway if you wanted to join a day tour, there are some public transportation options (buses and ferries) to other sights that you can get on your own if you don't want to join a day tour, or you could hire a private driver for just your group.
Lots of lively pubs, music and good restaurants in and around Galway.
Other option, head to Northern Ireland. You can easily get from Dublin by train or bus. Antrim Coast is scenic for some walks, easily accessible by regional commuter rail to many shore towns where you can stay overnight - during the summer, there is a free tourist shuttle that can get you to places like Giant's Causeway, Dunluce Castle, etc. You could also spend a night in one of the larger cities like Belfast or Derry, get a sense of history by seeing the political murals in the Catholic and Protestant neighborhoods and there are loads of pubs and good restaurants.