Hotel Austria or Hotel Kärntnerhof?

If this is the Hotel Austria you are referring to:
http://www.hotelaustria-wien.at/en/hotel-austria/

I can highly recommend. My daughter and I stayed there last June. We had requested twin room and we actually ended up with basically 2 rooms- 1 had the 2 twin beds, the other had a day bed/TV, plenty of space- they were connected via a small foyer with the bath area.
Anyway- it was great- excellent location- down a quiet alley very near the Alstadt and just steps to the trams and metro at Schwedenplatz.
Nice breakfast and helpful staff- also had AC which we actually really needed since it was in the high 90s!

As suggested to you as well on trip advisor, why settle for an ok hotel when you can stay at a great hotel? Booking.com has Hotel Sans Souci and Konig Von Ungarn in your price range on your dates.

Because the two hotels I'm asking about appear to meet my needs. If I couldn't find anything that appealed to me at the lower price point, I'd be willing to spend up to 300 euros. If I can find something I like for 200 euros, then I prefer to save my money for other things (a longer trip, next year's trip, etc). We're not luxury travelers and we don't spend a lot of time at the hotel. We just want a clean, comfortable room with breakfast included in a good walkable location and seemingly those hotels provide that.

As far as the hotels you mentioned, Hotel Sans Souci looks gorgeous but with free cancellation there is only a junior suite available on booking.com and it would be 400 euros a night. Even the non-refundable double room is at the very top of my budget
and I never book non-refundable rooms. Konig Von Ungarn is 254 euros a night and frankly the photos I've seen don't make it any more appealing to me than Hotel Kärntnerhof which is at about 200 euros per night.

Your choice. Have a great trip.

I booked some American visitors into the Hotel Pertschy last year and they were quite happy with it. It's around the corner from Michaelerplatz and the Stallburg.