Ballynahinch

Ireland is a good choice for a first-time Europe trip - basically no foreign language issue for English speakers, it’s beautiful, and the people are welcoming. I’ve been to Ireland on several trips, and done a fair amount of hiking there, although I’ve never been to Ballynahinch.

Some people use a travel agent (AAA auto club offers those services, as do others), but I and my husband book directly with airlines, hotels or Bed and Breakfasts or airbnb’s, and rental car companies, trains, and/or buses for transportation. It cuts out a middleman, and the Internet makes it pretty straightforward, as long as you’ve got the right Website.

Ireland’s got several airports: we’ve flown in and/or out of three - Dublin, the capital; Shannon, which is the closest to Ballynahinch; and Cork, on the southern coast of Ireland. Looks like a lot of airlines fly between Nashville and Ireland, including jetBlue, Southwest, United, and American, although there’s likely a connecting flight you’d have to make, and not many direct flights. Price might be a factor for you, too. Some airlines connect in Boston, flying from Nashville to Boston, then onwards to Ireland, others connect in Chicago, or you might fly direct from Nashville to Dublin (not Shannon), then need to get to Ballynahinch from there. There are a number of Websites that aren’t the airline’s itself, but that could give you an idea of flight times, prices, and routes, and then you could go directly to the airline(s) to actually book the tickets. For starters, see Kayak, Rome2Rio, or Google Flights.

Renting a car is not so simple, especially in a country where they drive on the left side of the road, including Ireland and Northern Ireland. First, if you’re jet-lagged, you don’t want to jump right into a car on the left side of the road, and take right off. You mob at want to wait at least a couple of days before you start driving there, and stay in your arrival city those couple of days as you acclimatize. Or use public transportation- maybe bus, train, or taxi or other private driver. Some roads in Ireland can be surprisingly narrow, and out in the country, you can be on a tiny road with a huge tractor coming the other direction. It’s common in Europe for cars to be manual transmission, and automatic trannys can be much more expensive - you have to confirm. Then there’s insurance, which can also be expensive. A few credit cards provide brace coverage against damage, but you have to check yours carefully first details. The rental company is happy to sell you insurance - at their price, so you need to read all the fine print. One company, My Irish Cousin, seems to go out of their way to make renting comfortable for Americans, including full insurance, but compare their prices with other companies like Enterprise, Dollar, etc. And are you ready to drive on the left side of the road, driving in roundabouts, with a stone wall just off the side of the road, traffic coming towards you on the right, and maybe shifting with your left hand? At least the gas pedal and the brake (and clutch) pedal will be to the left of it, but it takes time to sort that out. And dis try a nces cc and cc speed will be in kilometers, not miles- except Nirtgern Ireland, if you did go there, are in miles, like in the U.S.A. Like I said, not so simple.

Which Ballynahinch? Sounds like you mean the luxury castle hotel by that name in western Ireland, but there is also a town with that name in Northern Ireland.

Yes, I believe the hotel is in the county of Galway on the west. Not the town Ballynahinch.

If there is something more quaint and easy to hike from, I am open to suggestions. I’m trying to plan a little on my own for my wife as a surprise.

Thank you for all of your suggestions, tips and help!

From what I can see, Aer Lingus flies direct from Nashville to Dublin a couple of times a week.
As a starting point, I suggest researching the hikes you want to do. There are lots of good options available. Here is a website that can help:
https://www.theirelandwalkingguide.com
For hiking, I'd say any time from April to September, maybe October, but the weather in Ireland is notoriously fickle. You generally don't have to worry about it being too hot to hike there, so even high summer is an option.
Once you have identified some hike options, then you can begin to look at transportation and accommodation. I think the mistake a lot of folks make when planning a trip is to choose a city and a hotel and plan their activities from there. Maybe Ballynahinch IS a good place to stay to recuperate from your hiking holiday. I don't see that they have a spa, so for me, that wouldn't work. OTOH, for a lot of people, staying a night in a castle is a must-do in Ireland. You do you.
You might not need a car, depending on the hikes you choose. If you're not an enthusiastic "wrong side" driver, I say leave it to others. There are good train and bus services in Ireland, and taxis (or rented bikes) can fill the gaps.