Wow, what a whirlwind!! Awfully ambitious...
First off - I would vote for Budapest over Vienna any day... Vienna is a big, bustling city, lots of traffic, etc. Feels more like a city and less like an old world Empire capitol, although it still is. Budapest, however, fills that bill. It's a big city, too, but is a lovely city, and the river flowing through between the Parliament Buildings and the Castle on the other bank gives it more of an old world, even middle ages, feel. The Chain Bridge tops off the perfect picture. It has the old Europe ambience. It's a friendly place, walking around is easy, buy some of the beautiful embroidered Hungarian lace, (and it packs easy) and just prowl.
And I would only go here and Krakow if you're doing both. Sort of in the same area. I would leave out Athens and Hamburg. Unless you have family in Hamburg...? Not a stunning city. Athens and Greece are the destination for a whole trip in itself. Don't just see Athens and think you've seen Greece!! You have to allow time there to go to a few islands, and wander some of the countryside. Athens has a few good tourist sights, but the city itself is really not a gem. Most of the best tourist spots in Greece are far from Athens - Delphi, Temple of Poseidon, Corinth, Crete, etc., etc., etc., etc.... Athens is too far off the path of the other stops to make it worth the travel time and rush/rush it will cause you.
And do take into account that European unions have POWER and can choose to go on strike at the most inconvenient times. Meaning trains no longer run in some region, planes no longer fly, services like buses and subways may be out of commission. They don't care that you have a plane/train to catch... Allow some wiggle room because nothing, nothing, goes exactly according to plan. And that's one of the charms and joys of travel in Europe. Relax and wander, stay longer where you like it, leave quicker where you don't. You're too tightly scheduled here and you don't want to spend your trip just seeing train stations. Logistics - getting to and from transportation and hotels, is MUCH slower and more time consuming than it is in the states. Traffic, taxis, distances, having to walk to your destinations, etc. can make transfers take way more time. They don't have the same urgency in Europe that we do. And that's to be enjoyed, not fretted over because it's making you late, yet again...
Dial it back, have a relaxing but still fabulous trip, and start planning another to see the farther sights... ENJOY!!!!
Oh, and TAKE SOME BLISTER PACKS (buy them where you buy band-aids) and a small roll of athletic tape (roll some around a pencil stub or something) and maybe some moleskin. They'll save your life! With a schedule like this, you are going to walk your feet off! Prepare for that so that layers of blisters, which you'll get even from well broken-in shoes with this much walking, don't also slow you down. You'll have a great adventure!!