It is great to see you are heading our way.
In all honesty, if it was just the Giants Causeway you were aiming for I would say stay in Belfast. It is only an hour and a half from the city and there are loads of places to eat and drink in Belfast. The rules at the minute mean you can book and eat inside but if you are just grabbing a drink you will be sitting outside. Belfast has adapted to this well so there are loads of places including a few streets that are getting closed in the evening to allow the pubs to operate outside.
You do mention the coast though and if you don't fancy the idea of an hour or so in the car each way, I would suggest one of 2 places. If you are looking or a more peaceful experience with long evening strolls while you are doing the coast, Ballycastle would be the one. If you are looking for somewhere with a bit of nightlife to it, then Portrush would be for you, It also has some excellent beaches which make for a lovely evening stroll.
There are other options available to you though, so rather than just taking my word for it. Check out this article which gives you a breakdown of the best towns to stay in around the Causeway Coast.
Do let me know what you decide on, and if you have any other questions, I look forward to lending a hand.