Vienna and Salzburg -August or October?

With a 1 year old I would choose August...more chance nfor outdoor play. Of course, no guarantees.

First week of October. Few times the weather is better in Central Europe. And october is among the drier months: https://weatherspark.com/y/81358/Average-Weather-in-Vienna-Austria-Year-Round#Figures-PrecipitationProbability in Vienna. And 1 October temperatures https://weatherspark.com/d/81358/10/1/Average-Weather-on-October-1-in-Vienna-Austria#Figures-Temperature

I would absolutely choose October.

The Salzburg Summer Festival seems to run through the last week of August. I have never been, but get the impression it is a busy (maybe crowded?) time. I hope someone else can chime in.

October - you may have the opportunity to check dates for Almabtrieb (cow parades) in Tyrol or Bavaria.

Just sharing. These tidbits may not factor into your trip in any way.

Another vote for October. The Salzburger Festspiele ends Aug 30, as noted above, which will make the city more crowded the last week of August than the first week of October. I have been to Salzburg during the Festspiele and not during it; I can confirm that the city is definitely more crowded during the event. Hotel rates will be significantly higher during the Festspiele, too.

See, now you got me thinking I answered too fast. I should have asked if the OP looked to see what was going on in the city on each date and if it was somehthing they might enjoy. The Salzburger Festspiele would draw me back to Salzburg.

There are advantages to both, depending on your travel style , preferences, etc. For me I would go in the last week of August , better still the week before.

As you noted in your post, this is about the weather. And, what you want to do that is weather dependent, for example, enjoying an evening in a beef garden is an August, not an October event.

BTW, will you have a backpack carrier for your child? Parts of Salzburg do not seem to me to be overly stroller friendly.