That's too many places unless you primarily want to wander around and soak in the architecture and atmosphere (nothing at all wrong with doing that, but most travelers want to go inside things). Only you know why you chose those particular stops (well, I guess we know CK and Hallstatt are for their physical beauty). You need to consider what specific things drew you to each place. That's the way to figure out how much time you'll want to spend in each city, and how many stops you can fit into the time you have available. I do not count my arrival day at all (too sleep-deprived and jetlagged to function), and I figure the day I move on to a new city is probably just going to offer a few hours to look around casually.
Also consider the physical size of the part of town of tourist interest. It takes a lot more time to move around Budapest than around Salzburg. And trips out of town (e.g., to Auschwitz) tend to chew up most of a full day.
I'm a big fan of sites related to WW II and the Cold War, so on my recent trip to central Europe I spent seven full days in Krakow, not counting the day-trips to Auschwitz and Tarnow. It's a lovely city and I would be happy to return, but I did a good job of covering the sights of interest to me, and I enjoyed some casual strolling-around time.
I also spent seven full days in Prague (I love Art Nouveau architecture and have a special interest in Czech glass). I did not have time to do all the wandering around I wanted to do, looking at building exteriors; I basically just went from one museum/historical sight to the next. That's OK, because the country has a lot of lovely small towns I wanted to visit but didn't have enough time for. I'll have an opportunity to revisit Prague.
I spent seven full days in Budapest as well, plus a few extra hours, again not counting a day-trip (to Szentendre). A number of really important museums in Budapest were closed during my visit, so I did some (not all) of the just-walking-around I wanted to do. I also skipped some of the more minor museums I was interested in, because I knew I'd want to return when the key museums opened; I opted for some outdoor time rather than yet more museums.
It was a coincidence that I ended up spending roughly the same amount of time in Krakow, Prague and Budapest. Most tourists would need less time in Krakow. I didn't have time for Vienna at all and haven't researched it, but I'd guess that for me (lover of architecture and art museums) it would require at least seven days.
I always have a lot more on my plate than I can fit into my time allowance. My cuts are made primarily on logistical and weather grounds, but I do try to find out about special events that might interest me or--if they do not--drive up local hotel prices.
From the logistical standpoint I'd consider cutting Krakow in this case because it's just one of many, many interesting destinations in Poland. On the other hand, it is very touristy already and probably will become even more so in the next few years (I doubt that Prague is going to get much worse). Perhaps you'd like to see it before it is as bad as Prague?
Most of October will definitely be autumn in that part of Europe. Do some weather research on your proposed destinations to be sure you're OK with the likely temperatures and precipitation levels. You'll generally find a weather-summary chart in each city's Wikipedia entry; that's good for high-level comparisons. I've started using timeanddate.com to review actual day-by-day historical weather stats before making a final decision.
From Washington DC Munich is often the cheapest flight destination in central Europe, but I agree that you should fly into a place you actually want to visit. Krakow is a bit awkward to get to, so I'd try to fly in or out of that city.
