Trinity college is pretty cool, at least the Old Library and the Book of Kells. It's spendy for a ticket and a long wait in line if you're not there early, but how often do you get to look at a 1,100 year old book? However, across the street is the Irish Whisky Museum and for 20 euro, you get a tour, a thorough explanation of Irish whisky types and three pours of various styles - it ain't just Jameson.
The Dublinia Viking museum has some nifty stuff on display and a history of Dublin. Christchurch Cathedral is directly across the street. Not far from there is the Brazenhead Pub, which is a bit touristy, but it maintains the status as Dublin's oldest pub (1295). All of that is pretty close to the Guinness Brewery and St. James Gate.
Dublin is a small city and you can walk a fair amount of in a day.