Italy and Austria - three weeks in Sep or Oct

sharon,

Given the relatively short time frame of your holiday, I'd probably skip Torino as it's somewhat of an "outlier" in the overall route. It's important to allow some time for travel between locations, which in some places will be the better part of a day.

Regarding your questions......

1. My suggestion would be to use trains, as well planned rail trips are often the fastest and most efficient travel method (especially when using the high speed trains which travel at up to 300 kmH). This will also be less expensive if pre-purchased tickets are used.
2. Especially for travel in September, pre-booking rooms would be a good idea as it's usually quite "busy" in Europe. If you want a more "spontaneous" approach, you might check the guidebooks, as there are listings there for reliable accommodations in each of the places you'll be visiting (except for Torino). You could make a list of 4-6 places in each city, and hopefully one of them will have a vacancy.
3. I'd lean towards September, as the weather will likely be better (although of course no guarantees).
4. Check the RS guidebooks for each place you'll be visiting. You should be able to find reasonably current copies in your local Library or larger book stores.
5. I'm not sure you have time to stop in "between" cities. I'd suggest staying with the cities you have listed, and then perhaps add a day trip or two. One very popular day trip from Rome is Orvieto, as it's only about an hour each way. An easy day trip from Florence would be to visit Siena (use the bus on this route).

Have you travelled by train in Europe before? If not, you may want to read the "Rail Skills" chapter in Europe Through The Back Door, as there are a few things to be aware of. Some rail trips will involve "changes" and you'll also need to be aware of which stations you'll be using (many cities have more than one). You'll need to be especially careful in Italy, as there are some potentially expensive "caveats" to be aware of when using public transit (trains, bus, metro). If you need further information on any aspect of this, post another note.

Ken has given you great advice. I would only add that September is still hot and crowded in September and October tends to be very nice. Perhaps start your trip in mid-to-late Sept ar the earliest.

I envy your desire to be spontaneous, but would caution it can be hard to find a place in Roma, Venezia and Firenze (you need to use Italian names for train reservations) on the spur of the moment. You can usually reserve on Booking.com with an option to cancel a few days in advance. You might want to hedge your bets by having some rooms booked and then modifying or cancelling as you go. Certainly make reservations for your first stop in Vienna.

Ken has given you good advice. Torino will probably be out, as it's in the far northwest--close to France and Switzerland.
I agree about using trains for travel from city to city.

Booking.com and other large websites are great places to look for rooms, but you probably want to make reservations at these popular tourist cities. $75 a night for lodging average is probably a little low, as 70 Euros is more the bottom line for a decent place in Europe. Great cities can be even higher. You might look at AirBnB.com to see if they have properties in your price range.
September is the preferred month unless you were going to Tuscany for an agriturismo. The big harvest is in October.

I've been in Italy in late September to late October in a number of recent years. If you want reasonably-priced/safe/nice-enough hotel rooms on the spur of the moment at $75 or even 75E, particularly in cities like Venice or Florence, you may end up being well away from the historic center, if that's OK with you. Or you may need to turn to hostels. In Venice in the latter part of October a year ago, finding a place 3 months ahead of my arrival took some effort, since I needed 5 days, central, clean, en-suite, and less than 100E/night for a single. Convents were booked or were already filled with student boarders. I'm not interested in a hostel. I sent about 20 queries and found a room in a very simple. very basic hotel near San Marco for 90E.

Monasterystays.com and booking.com can show you what is available at the last minute, but in the fall, I've usually found the location of last-minute budget hotels to be less than terrific.

To Everyone who has taken the time to reply...

Thank you so much! Your insight and suggestions are wonderful.

As of today, my wife and I are planning to limit our visit to Venice, Florence and Rome. We will book our rooms in advance (probably thru airbnb) and we will book the trains in advance to get the best rates.

We really appreciate your input!

Thanks

Brian and Sharon

ps. We've also learned thru this process that we need to book our flight as soon as the flights are available (about 330 days in advance?). We are finding that there are very few flights available which will allow us to use our frequent flier miles.