think about Lisbon, we often go there for a short break.
There is a lovely old fashioned tourist tram from the central square in Lisbon that will take you up the hilly part and all around the central part of town, its very relaxing, never rushed and good fun.
You can catch the ferry boat [ about 50p] over water and go and eat where the locals go to eat at fish restaurants [ avoid the "touristy" fish restaurant area in central Lisbon - too expensive.There are many coach to tours available, try one to Fatima and the one to Obidos, from the train station [ ask because there are two] you can go to Cascais for the day have a stroll around and a nice open air meal and return in the evening, trains are clean and comfortable and on time.
For the more adventurous go by train from Lisbon to Porto and stay there for a few days, visit the wine lodges etc.
We dont book a hotel, but go to the tourist board in Lisbon airport on arrival and they book for us.
just an idea.
Maderia is very nice for a quiet holiday, but you may find it too hilly. Dublin is good too, but not the weather always.