Our personal preference has been to find ourselves a base for a week, explore what we can within driving distance, and then plant ourselves somewhere else. We generally go for a month at a time which isn't possible for a lot of people. We've always enjoyed each area and try to get the most out of our time.
Our Galway trip included:
1) took the ferry to Inish Mor and rode around the island on ebikes, enjoyed the views from the cliffs
2) spent a day walking around the old part of Galway City and visited a pub, went back to catch the service at the Cathedral
3) went on the Hawkwalk at Ashford Castle, walked around the grounds and visited the village of Cong next door (we also had a private tour of the castle but it's not normally open to the public-it's definitely on our bucket list to go back and stay there). We later went to dinner at the Pulman Restaurant at Glenloe Abbey Hotel just north of Galway City. The restaurant is set in old rail cars from the original Orient Express film (our son is a big fan).
4) took a drive around Connamara, stopping at Kylemore Abbey, and driving the Sky Road- beautiful views.
When we stayed in Derry a couple years ago:
1) took a walking tour of the walls which was quite informative, and just explored the older city that has several small museums
Both my husband and my families came from there so there was a lot of exploring cemeteries, etc.
2) it was an easy drive to the Ulster American Folk Park in Omagh from there, which was interesting
I always look to see what is going on in the area. I lucked out a few years ago and visited Derry during a cultural event when they had all sorts of reinactments of the Siege of Derry. I found it helpful to read up a bit on the history.
Derry is a busy town but I really enjoyed the history.
In April, we needed a place to stop between Co. Tyrone and Galway for a night to break up the trip. We visited Slieve League cliffs (similar to the Cliffs of Mohr without the crowds) and stayed at Slieve League B&B. We took a short hike from the B&B to the edge of the cliffs-absolutely beautiful with sheep everywhere. We also went to church in Killybegs, not realizing that the mass was being said in Gaelic- didn't have a clue what was being said but enjoyed it, just the same. I understand you can take a boat ride to the base of the cliffs but we didn't have time.
We've also stayed in a really small village called Clonmellon, in Westmeath. a couple different trips. It's only an hour from Dublin and was handy for visiting Newgrange and many historical sites. The place we stay is a converted stone carriage house owned by a wonderful family that has a sheep farm so there's usually animals around. We spent one day and visited a distillery in nearby Kilbeggan and another day, we spent all afternoon learning fly fishing. (arranged by the owners).
Right now I'm trying to plan our September trip- a week outside Waterford, a week in Kinsale, a week outside Dingle, and then a week in Wicklow. We try to stay at self catering cottages because we have an adult son along but B&Bs are my favorite if there's just 1 or 2 of you. We're a little older than you but like to be active. Not golfers, but cyclists, so we plan to rent either regular bikes or ebikes.
I don't know if this has helped or confused you but wherever you go, you'll enjoy it.