Dublin has become an expensive city, so think twice if your main goal is to save money!
Some posters on this board don’t like Dublin much, and I’ll have to confess that my bias in favor of Dublin comes from having lived there for 4 months while I was a student. These days, I often stop off there when I’m flying to Europe because I can see old friends and a cousin there, and also because I can recover from a long flights from the western US before I go on to Europe.
One of the many things that I like about Dublin is that it’s a pretty compact city, so that you can walk around and see quite a bit in one day (by the way, can you give us some idea of roughly what your arrival and departure times might be?). Remember that you’ll have to take into account time collecting luggage and getting from the aiport to town and back again—- and wasted time caused by not being familiar with a strange city.
I think that, rather than going to the Guinness Brewery, you’d be better off going to a pub for an “authentic” pint of Guinness, and maybe some food, something like smoked salmon wih the Irish brown bread.
If you use public transport from the aiport, you’ll drive along O’Connell Street and, frankly, there’s not much to see there except the GPO (post office), which was the headquarters for the overthrow of English rule.
From the O’Connell St Bridge, you could walk a short distance along the Liffey to Ha’penny Bridge, cross over to Templebar, then to the Bank of Ireland (formerly the Irish Parliament), then across the street to Trinity College, where you could see the Book of Kells, then perhaps up Grafton St to St Stephen’s Green, along Baggot St to Merrion Square, past Pearce Station back to the River Liffey at about the Custom House. You could easily do this in 2-3 hours, even with stops, and you’ll have seen a lot of central Dublin fairly quickly.

Sarah writes:

There’s no Guinness factory; It’s called a brewery!
Basie gives you a pretty good description of what you might be able to do in Dublin w/a 1-day layover.  The only thing I would add is a Carvery lunch at one of Dublin’s famous Pubs.
 
You’ll probably spend that $25 you save on Excess baggage charges on RyanAir since your stopover in Dublin means two RyanAir flights;  and you’ll have to pay the Excess Baggage charge on each.   So, it’s a ‘wash.’
 
I have visited Ireland many times and Dublin is not among my favorite European cities (Madrid is), so I would bypass Dublin and take the nonstop to Madrid.  One flight = one excess baggage charge.