You will have to buy a ticket for the Austrian portion of your trip — I assume that’s the in the trip planner.
Renting a car isn’t a terrible idea. It is, however, an expensive one and, IMO, having a car in a some of the huge cities you’ve listed will be an expensive nightmare. I’d seriously look at renting a car for part of the time in Italy to explore some more rural places, but the Rome/Venice/Florence connection is faster and easier by train. You can’t have a car in Venice and you won’t want one in Rome or Florence. You might also enjoy a car in Ireland, although you might not have enough time there to make it worthwhile. I’ve read that Dublin has some of the worst traffic jams on the planet — didn’t notice it when I was there, but I wasn’t driving. I would agree — especially after you figure in the travel time to get to/from and around Greece. Spend some time with ferry schedules to see how much time you’ll actually get to spend on each island. You may have to check-in for the ferry two hours before departure, so check those requirements, too.

Thanks so much for the reply, I hadn’t considered the ferry times in Greece. We may have to cut it down to two islands in order to fully enjoy our time.

As far as overnight trains go, is that an additional charge or will that use up two days on our Eurail? We’re definitely looking at staying in hostels and is it recommended booking them in advance or is it just as cheap to show up the same day.

Also, other than the museums and Guinness Brewery, what else would you recommend in Ireland in the short amount of time we’re there. Is there anywhere near Dublin that would be worth driving out to, or since we’re only there for two full days should we just explore Dublin as much as possible?

Thanks for the help, any information you can provide is helpful!

Most overnight trains only require one day of the pass. The “7:00 PM rule” allows you to use only one day of your pass (arrival day) if a train departs after 19:00 and arrives after midnight. There must be no connections before midnight. There’s usually at least one train that fits this between major cities.

All overnight trains require reservations which aren’t covered by the pass. Expect to pay 10 to 12 euros for a reclining seat (available on some trains), 20 to 30 euros for a berth in a 6 berth couchette and 30 to 40 euros for a berth in a 4 berth couchettes. The various single and double rooms available can get very expensive.

You can spend a reasonable 2 days in Dublin and I wouldn’t try a day trip in that time. If there’s something outside Dublin you must see look for an organized tour or work out the details of a day trip in advance and do it your 1st full day there. There are some decent places to chill in Dublin, like peoples park and any number of pubs, which will be good for jet lag/sleep deprivation recovery. Personally, I’d seriously look at cutting Dublin for a more reasonable rest-of-the-trip.

Given your tight itinerary and the fact you’re traveling in August, I would book hostels in advance. August is the absolute busiest time in Europe as that’s when almost all Europeans go on vacation.

I posted a response about the itinerary on your eurotrip page.
For your question about hostels vs hotels:
You may want to get a private room in a hostel rather than a hotel room. This gives you all the options of a hostel (social atmosphere, pub crawls, possible free breakfast, most likely free Wifi) that you don’t usually get in hotels.