Edinburgh is a really nice city to visit. I have been to Dublin three times on 'day trips' and it can definately be done in a day (well, the city centre at least!) and an open top bus tour is probably the easiest/quickest way to see everything. You can get cheap flights there from most airports in the UK. Ryanair (ryanair.com) usually has flights for 5-10 pounds each way including tax (i'm not joking. i paid 5 pounds last time including tax each way!) if you want to go budget airline and the flight is around 40 minutes, though security can take a while depending which airport you go to. Aer Lingus also has inexpensive flights, and you can fly to Edinburgh from London easily too, though the train is much more scenic! You ought to go to Ireland if you get a chance, I heartily recommend Belfast if you can't do Dublin...they are both very different but fun cities to visit... Good luck!