Sorry, I missed this thread up to now. I loved western Hungary long the Danube and covered a bit of it in
this trip report (not sure what's happened to the pics, sorry). I love both scenery and history, so it might be a bit biased towards Cathedrals for what you are after. Probably not enough to sustain a week as well.
I found one of the best wine restaurants ever in the centre of Budapest -
Klassz, on Andrassy ut (street). That's a few years ago, so I hope it hasn't changed much. The counter was a plank put across a bunch of wine barrels

. There is a lot to see in Budapest - you have to get some historical buildings in! Great views from the Castle; the Parliament building still has bullet holes in from the revolution ...
Taxi drivers are particularly manic ...
But if you want beautiful, scenic places, hand you have 'done' Austria and the Czech Republic, then I would recommend Romania, and in particular Transylvania. Easy to get to from Budapest. I flew to Sibiu from Vienna on Australian Airlines. Romania part of that
trip report here. Again, sorry, the pics have gone. But the Carpathian Mountains are spectacular - and you will still squeeze some ancient castles and fortresses in! (Dracula's castle is OK, but many more are better). Again, fantastic wine place in Brasov - Terroirs

That trip was also history focussed, but it included the scenery as a by-product. if you want to go scenery, there is it in abundance. I did a tour in a car, and it was really terrific. Costs a bit more, but you get so much more out of it, especially the convenience on not worrying where/how to park and how to dodge the maniac who's coming at you from the other way! if you are interested, PM me and I'll give you the name, and the driver/guide, who I couldn't praise enough for commentary, knowledge and driving.
Croatia of course gives you the Dalmatian Coast, which is spectacular, but mainly from the water. I drove down the coast and the road is awful and you don't get to appreciate the coast as it should be. plus I think its too long for the time you have.
Slovenia is called 'Switzerland in miniature'. Its the eastern end of the Alps and again, spectacular, but very compact. Look up Lake Bled. A drive from Budapest down to Zagreb and then up to Slovenia might be an idea if you don't want Romania.