Stroll around the Liberties or stop in The Brazen Head, Dublin's oldest pub!
Walk around the campus or check out the Old Library
You can take the Enterprise train to Belfast from Dublin which will only take you 2 hours and will cost you 13 euros. https://www.irishrail.ie/en-ie/Offer/take-the-enterprise-service-to-belfast
Recommended by our wedding officiant! Been around since 1798!