Christmas markets

I think I would start in Prague, go to Vienna and end in Budapest.

I would start in Prague and go to Vienna and then to Budapest, or the other way around. I would also take a day from Prague and give it to Budapest. Good bet for a hotel in Budapest is the K&K Opera. Really well situated for seeing a broad cross section of the city efficiently and provides great evening walking....

Look at a map. Vienna is about half-way between Prague and Budapest. If you fly either in or out of Vienna, then you'll be backtracking. Train journey from Vienna to Budapest is a little less than 3 hours, to Prague is 4 to 4.5 hours, from Prague to Budapest is 6.5 hours.

I think 7 days is not enough for all 3 cities. You won't have much time to enjoy the markets if you focus on the sights, or the sights if you want to spend time at the markets. If you choose only two, you could also visit Bratislava as a day trip and have time to enjoy both the markets and sights of Vienna and either Budapest or Prague.

Frankly, if you are interested in Christmas markets travel into the opposite direction. The Christmas markets in Czechia and Hungary were established in the last 20 years to promote tourism, they aren't part of the local culture. To understand what this means see a Christmas market in a smaller town too, which is not overrun by tourists but mostly visited by locals. That's a totally different atmosphere. And three big cities in just seven days is too much anyway.

In my notes, I had myself flying into Prague and out of Budapest with a stop in Vienna along the way.... somehow got it wrong here ;) I know that it is a lot to cover in 7 days but I will be by myself this time and feel that I can do it. I may look at this again. Most likely, this is an area that I will be coming back to at some point. I know that the German markets may be more authentic but just not where I want to go at this time.

Thank you to everyone who has responded so far

Can't speak to the markets in Vienna or Prague, but the one in Budapest is regulated to help ensure Hungarian made craft products. The few times I've been i have enjoyed.

Thought Vienna was German but choose not to unite with the other regions in the 19th century? Fred?

In 2016 we spent Christmas in Budapest. We spent several nights in Prague on the way to Budapest. Much of the stuff in the Christmas markets in Prague was made in China. Very tourist trappy! The Christmas markets in Budapest were far superior. The stuff was locally made and the locals were buying it. Not tourist trappy!

I would suggest that while you are in Prague and Budapest to take a cooking class. You may find it to be a high point of your trip!