I spent 2 days in Belfast as part of our Antrim Coast Trip last year. I went on to Dublin from Belfast by train and it takes just over 2 hours, so taking a train to Belfast with a return can be done quite easily. Connaly Station in Dublin is where you will start and the train will roll right into Belfast Central Station (now called Lanyon). I do not think you will need to grab a cab to get to the titanic museum unless you have mobility issues.
I would recommend heading to St George’s Market upon arrival, which is a nifty indoor market that we enjoyed. It is just a block or two from Lanyon Station. Then, I believe another mile or so walk along the river to Titanic Belfast-which was enjoyable and worth a day trip from Dublin.
Other pubs or restaurants I would recommend:
Mourne Seafood Bar, a place I read about on this forum which I wholeheartedly second the previous posters recommendation.
The Crown Liqour Saloon-one of the oldest pubs in Belfast, with a lot of interesting features.