#1: a water-resistant coat. I have a small, foldable umbrella but I hardly ever use it; if it's raining hard enough that I want it (more than a drizzle) then it's usually so windy it will just invert anyway, or be a problem.
@Imma 's tip works for Dublin, too: if it's raining, duck into a museum or into a coffee shop, and by the time you have had a little break, the rain will likely be over. (for the moment)
I'm not sure I agree with
@ObviouslyNotAGolfer 's observation on timeliness in Dublin. Maybe for tourist buses, but time here among natives is always "-ish." as in, "I'll see you at 3-ish." without the "ish," that means 3:15. With it, maybe 3:30. Even the airport buses are +/- 15 minutes, and they run every 30! You definitely want to have the various apps for public transport (Dublin Bus, LUAS, and DART) for accurate times.
That's another point for Dublin: a rare European capital without a train connection from the airport to the city center. But there is decent bus service: as fancy as you want, although the Dublin Bus / public pus routes 747 and 757 are just fine. The city buses are also double-decker, so get yourself in the front of the top deck, and have a free little tour. (But do be on your toes for your stop, though--head downstairs beforehand.)
One thing on wardrobe: washers and driers in Europe are
tiny compared to the US. If you bring jeans, one pair might be the whole load. And quite likely, you will have a combo washer / dryer, so you can't double up through both machines. Laundry can take *a l o n g t i m e* so quick dry is your friend, even without the weather. Think in terms of 1/4 your US washer capacity, and 3 hours per load--it's time management as much as weight. Also, there aren't a lot of laundromats here in Dublin, but there are a lot of drop-off laundry services. So, if you want to save time, you may also want an identifiable laundry bag to drop off. (if you do self-serve, there are a number of machines in the open air at gas stations. Shocking to see, at first glance) You will definitely not be able to do 6 days' clothes in an evening. I would rather suggest packing for 3 or 4 days, and doing it incrementally (when you leave for the morning, before going to dinner, or overnight) or splurging on a laundry service to do the work for you. Finally, if you are sensitive to fragrances, bring your own detergent. It seems clean = reeks of flowers or fruit here. Very difficult to find unscented detergent; it's one of the things we bring back in bulk from the US.