A great way to see the city is to catch a hop on hop off bus tour. Open top buses are stroller accessible (although you will have to carry your baby to the top deck) and offer a great way to get directly to the main sights without having to worry about public transportation, tickets and crowds. Viking Splash Tours offers a fun alternative to the double decker bus, where you are taken around the city in a giant viking longboat however, this is more suitable to older toddlers and under 2s are not permitted on the tour.
Dublin City Tours
A great way to see the city