Self Drive Best Option?

Why not ? I was 77 on my last rental in Northern England and Scotland ( ten week trip , five weeks with a car ) and I would do it again without pause , I'm 80 now

It depends on how confident you feel driving on the left, and possibly with a stick shift.
We are not much younger than you and when hiring a car abroad, we always go for an automatic as that's what we have at home and it means we have one less thing to think about driving on the "wrong" side of the road.
Most Hertz locations seem not to have a upper age limit.
Unless you are used to electric, you might want to think about sticking to petrol/diesel, or a hybrid.

We have driven a lot in Europe. Lately we've been visiting countries that drive on the "wrong side" of the road--England, Australia, New Zealand. Next up, Ireland. We've adapted quite well, but for those countries, we've insisted on automatic transmission, elsewhere a manual was fine. We felt like in a stress situation, when something happens because of the surroundings or another driver, having a manual transmission would just complicate response. Remember, you will also be driving on the other side of the car.

With your good health and driving record, I think driving would be fine. One thing we always do is try to pick up and drop off the car in a smaller city, or less busy area. We'll take public transportation to the car pick up location.

We are still in our 60s, so not an issue, but lately when arranging rentals, a few companies have been asking if over 70, or charge more, so its good to make sure to state age before finalizing rentals.

How about doing a combination of public transport and car? Take the train to Coleraine and rent your car there away from city hub-bub.

If you're a confident wrong-side driver, have at it! So much to see there. Depending on how much time, if any, you plan to spend in Belfast and where you plan to stay, you might want to wait on picking up the car until you're done in the city. OTOH, if you're flying into and out of Dublin, picking up and dropping off at the airport is probably the cheapest option.

It's ironic , It is the correct side in the UK . Every time I return from a trip to the UK, since I always drive ( though not in the big cities , where a car is a nuisance ) I find myself having to stay on the right side of the road at home .