Need itinerary help

In my (very biased) opinion, none of your proposed itinerary visits (Wachau Valley, Melk, Durnstein, Linz, Passau and Cesky Krumlov) are nearly as interesting as the city you will be traveling to - Budapest.
And yet, ....."As soon as we arrive in Budapest, we would like to take a train or bus......"and go somewhere else.

Not me.
As soon as I arrive in Budapest, I kiss the ground.

Hi, I love how passionate you are about Budapest. From what I have read, it is truly an amazing city! Given the amount of time we have and all the places we want to see, I had to make a decision -do we see a lot of one place or a little of multiple places? I really wish we had more time to stay and visit to our hearts content.

Okay, the only thing i know for certain is that the trip is all over the place. I do know what i think is the best direct route from Budapest to Cesky Krumlov: https://www.ckshuttle.cz/transports/transfer-from-budapest-to-cesky-krumlov/

And I do understand wanting to see more than just Budapest. Let me suggest you google "Slovakia Castles" and "Eger Hungary" and "Pecs Hungary" and "Pannonhalma Archabbey" and "Gyor Hungary" and "Banská Štiavnica" and "Banská Bystrica" and "Szentendre" and "Esztergom" and "Visegrad Hungary" and "Sopron" and "Kecskemét" These are all places within close proximity of Budapest and will replace travel time with sightseeing and enjoyment. Just do Google Images and see if anything pops out that is interesting.

Or, go way afield. Go to Google Flights, put in Budapest as a start, Europe as the destination, then choose one way, non stop, with a maximum cost of say $100. Now you can see where all the discount airlines go. Most under 1.5 hours flight time and quite a bit of fascinating Eastern Europe opens up to you. Normally i will fly into a place like Sofia or Kyiv or Tirana or Podgorica; spend a few days seeing the area, then catch a dicount airline into Budapest. Or you can spend a few days in Budapest and take a cheap flight to see some new exotic place, then fly back to Budapest for a few more days.

For quick side trips, check out of your AirBnb and put the heavy luggage in a storage locker; Like Lion Locker on Vasvari Pal utca in Budapest then check back in 3 days later. https://www.lockerbudapest.com/ (good breakfast too)

It is also my (very biased) opinion to follow the advice of James E.

Thank you James and Blue for your wealth of information and suggestions. My trip is looking much different now :)

Yep, I spent 3 weeks in Budapest last November and followed much of James's suggestions, but 20 of 22 nights were spent right inside Budapest and I enjoyed every minute!

Here's what I did last September. Long weekend in Budapest, then left my suitcase at the hotel and took an overnight bag for 4 nights. Train to Pecs (2N), bus to Szeged (1N), train to Kecskemet (1N), train to Budapest for another long weekend. Great food, excellent wines, beautiful architecture, and so much more, including opera in Budapest.

I will second what Blue439 said. Just do what James E says. He knows of what he speaks.

My husband and I will go with the general consensus and spend the first 5 days of our trip seeing other places in Hungary, before our Budapest tour begins. I read up on the places James mentioned and I like all of them ("Eger Hungary" and "Pecs Hungary" and "Pannonhalma Archabbey" and "Gyor Hungary" and "Banská Štiavnica" and "Banská Bystrica" and "Szentendre" and "Esztergom" and "Visegrad Hungary" and "Sopron" and "Kecskemét"). Someone else mentioned Szeged and Kecskemet. The question now is, where to stay. Do we stay in Budapest and take day trips or are there a couple of other central locations to stay to maximize the time and make transportation easier? Also, is there enough time to see all these places in 5 days? If not, any suggestions on prioritising them will be welcomed. Thanks in advance.

I'd rent an apartment in Budapest. All the trains go through Budapest so it's hard to go from A to B without returning to Budapest. Just leave your stuff and every couple of days run off and see something with a day or overnight bag.

Eger, one or two nights
Pecs, one or two nights
Szentendre is a day trip, up on the commuter train, back on boat
Gyor, and the Archabbey, either overnight or a day trip.

Minimum 5 full days in Budapest.

Ten days goes by fast......
If you rent an apartment and play it a little loose you can decide a lot of this when you get to town. The apartment will cost you $60 to $75/night for a nice place in a good location.

1. Saturday Arrive
2. Sunday Budapest
3. Monday Budapest
4. Tuesday Morning Budapest to Eger 5, Wednesday Eger
5. Thursday Morning Eger to Budapest
6. Friday Budapest
7. Saturday Budapest - Szentendre - Budapest (boat gets in about 6pm)
8. Sunday Budapest
9. Monday Budapest home

Train rates and scehdules: http://elvira.mav-start.hu/

Eger, one or two nights. Train to Eger in 2 hours for about 3.000 forints. Stay at the Senator Haus Hotel. Best location in town.

Pecs, one or two nights. Train down to Pecs takes about 3 hours. Fare is about 4.000 forints. The only hotel i have stayed at in Pecs was Hotel Palatinus City Center. It was a grand hotel .......... once upon a time.... now... well, BUT, i love the character and i love the locations. I would do it again.

Szentendre is a day trip, up on the H5 commuter train (https://bkk.hu/en/news/), back on boat (http://www.mahartpassnave.hu/en/timetable/danube-bend-excursion-boat-lines/budapest-szentendre/) Total Transportation Cost is about 2.800 forints round trip. About 30 minutes to Szentendre and 45 minutes back on the boat.

Gyor, and the Archabbey, either overnight or a day trip. 1:20 train ride (no more than 3.000 forint per ticket). Stay at Hotel Klastrom. Taxi to Archabbey, maybe $20.

And I forgot Tihany. I love Tihany on lake Balaton. Well worth a night. About two hours on the train and 3.000 plus a small taxi fare from Budapest.