November wouldn't be my choice for a trip north of the Alps, but I really, really don't like chilly, wet weather. Most people don't seem to mind it too much and appreciate the less-touristy surroundings.
How many nights do you have on the ground in Europe?
I think you're overestimating the time you'll have in each country. To have 3 days in Prague, you'd need 4 nights; for 2 days in Budapest (which you will surely find extremely inadequate), you'd need 3 nights. There's no way that leaves you with 8 days for Austria. Moving from city to city is going to chew up at least half a day, and if you end up needing to travel between Prague and Budapest, the train alone will be 6-1/2 hours, not including time dealing with hotels, getting to and from trains stations, etc. And all for way too little time in the city. So I'd drop Budapest, saving it for another trip when you can give it the time it deserves.
You'll save some doubling-back time if you can fly in and out of different cities, but you'll need to check fares to see whether that is financially viable. The best gateways would be Prague and Budapest if you want to keep all three countries on the itinerary.
Edited to add: To look for flights in and out of different cities, select the "Multi-city" option on your chosen flight website.
