hi macca:

I did the reverse trip last year. We stayed in Budapest for 4 nights and loved it, day trips outside the city were very accessible by train. We flew SkyEurope at the time, not certain they fly into Dubrovnik now, you can check online, but it was very quick and easy.

Food in Budapest is excellent and my favorite of the entire trip, very rich, sometimes spicy with all sorts of unusal items, i.e. pork marrow at Mensa - delightful. There is a large central marketplace which looks like a converted train station, perhaps it is - Vásárcsarnok Market with all types of food items on the ground level and all sorts of food kiosks on the second level with plenty of crafts as well. If you are so inclined go to one of the spas, they are lavish and exotic - my partner would not go so perhaps my next trip.

We also stayed four nights in Dubrovnik. There are a number of SlowTravel or SlowFood restaurants within the walls - the snail or the turtle is indicated on the menu board - can't remember which one. I would have to say our best meal was outside the walled city at one of the restaurants heading toward Lapad called Levenat which was the most expensive of the trip but we found it reasonably priced with wine. Don't miss a walk around the walls and the beautifully restored town.

Depending on where you are traveling from 10 days should cover these two places with a day trip of two.

Thanks Denise.Your suggestions will be invaluable, and we will certainly try to capture some of the pleasure you had.
Perhaps I was not quite clear in my post, but we have ten days between the time we spend in Budapest and in Dubrovnik.
ie we have time in each of those cities and are looking at palces and things to do/see on our way between the two cities

Gotcha macca:

10 extra days between Dubrovnik and Budapest.

I would visit Montenegro for a day or two, Budva and Kotor - the border is about an hour outside of Dubrovnik, you could day trip or longer in Mostar, Serbia. Into Hungary I would if I had the time again travel the Danube and stop in Pecs for a few more days. All the things I wished I could have squeezed in on my trip.

If you're seriously into wine, you can't neglect Eger and the Tokaj-Hegyalja region. It's more than a worthy detour.

I doubt you have time for cycling given your ten day time frame, but here's a post about experience in the wine region...

http://www.luxepacker.com/files/cycling_hungary.html