Skip the Jungfraujoch. Way overpriced and touristy. And in high season, very crowded. With shops. Unless you've never seen snow, I suppose.
Much better in the Lauterbrunnen valley (one of my favorite places to be) is do some ridge walking. Either up to or down from Piz Gloria on the Schilthorn, (more strenuous, but real ridges) or Mannlichen (above Wengen) to Kleine Scheidegg. Very easy walk. Take most of the Jungfrau train back--but the cheap part.
2-year former Dubliner here. So much to say about what to do in Ireland. Highly recommend 2 years there. :)
If you see the Book of Kells, either book ahead, or take a student-led campus tour. The tour includes your ticket, so you can have an interesting prelude vs. waiting in line. I personally like it just for the Long Room, not the Book. Take a look around the Long Room. It's not just a Library; it's the Smithsonian, too. There is a copy of the Irish declaration of independence, and THE Irish harp (Brian Boru's harp) among many other artifacts.
Grab a pint of Guiness at the Gravity Bar at the brewery. Irish judge the quality of their pint by the distance of the pub to the brewery, so there is no fresher.
The busking on Grafton Street is top notch. Dublin is a blast from the past retail-wise, with many books stores and record stores, even a real Tower Records on Dawson Street, one block over.
The restaurant scene is Dublin is bountiful. I highly recommend KC Peaches for good eats, cheap, by Trinity. (Assuming you don't mind fast casual, as opposed to sit down)
The Cliffs of Moher are spectacular, but hard to bet all-or-nothing on your time. Any Irish site could be cloudy or fogged in. Best bet is to diversify and enjoy the one that got the weather right. I do like both the Aran Islands and Connemara, too.
If you are adventurous, you might try driving instead of taking the train. I was scared to death to try right-hand drive, but it felt natural pretty quickly. I still have my Irish driver's license. DW tried it twice, and said "Nope." If you do, take the slow way; avoid the motorways and take some A and B roads there. Lots of curves, narrow paths, hedge rows, and country scenery. Wait for a herd of sheep or cows to clear the road. Stop at a little town's only pub for lunch. Strike up a conversation with some strangers over a pint. That is as much Ireland as any sight. (They might comment on your accent, too)
Never been to Mullingar, but our go-to garden is Powerscourt. Voted 3rd best in Europe, after Kew and Versailles. Avoca runs concessions at many Irish historical sites. They also have a few locations in Dublin, and are good fast-casual with a variety of choices.
