Depends on the cities... got any of those in mind?
RyanAir is typically the cheapest way between Ireland and the UK, and there are cheap-ass flights on EasyJet and BMI as well.
There's also rail and bus, which can be reasonable, but there's a bit of water separating most of the two countries, so you're looking at a pretty long ride.
There's the bus/rail and ferry combo, as well, which can be cheap depending on when you book and what ports you use.
As far as value goes, I say flying's the best way - it's pretty cheap and it's fast. Rail is good if you're going to go all around, say Shannon -> Dublin -> Belfast -> Scotland -> London - or something like that.