Hotel recommendations in Vienna and Salzburg

Vienna - Hotel Pension Suzanne. Just around the corner from the Opera House and just off the pedestrian corridor towards St. Stephan's church.

Salzburg - Hotel Turnerwirt. It's out of the town center on the Northeast side, but nice rooms and at the low end of your budget. 4-minute bus-ride or 30-minute walk to old town and near bus that goes out to Salzkammergut Lake District. In addition to all the city-center sights, rent a city bike from the waterfront across from Mirabell Palace and ride along the Salzach River to Schloss Hellbrunn.

Vienna -- I have also stayed at Hotel Pension Suzanne and can recommend it. It would be at the upper end of your range. It's near the Karlsplatz U station. The owners speak excellent English.

Salzburg -- Gästehaus in Priesterseminar Salzburg. The priest seminary business apparently isn't what it used to be, so this seminary rents out spotless, updated, simple rooms (without TVs but with en-suite bathrooms) at a good price. Location is just across the river from the Old Town (perhaps a 5-minute walk to the Old Town) and about a 15 minute walk from the train station (can take a bus or a cab, too). The walk to the Old Town feels very safe even at night. Good breakfast. I have stayed there twice and loved it. All the front desk people speak English except one daytime person (but she usually works with someone who speaks English).

What are your dates in Vienna? I’ll be happy to see what is best on the days you’ll be here.

I’d also like to note that trains to Salzburg no longer just leave from Westbahnhof. Westbahn Trains on for salzburg leave from Praterstern, Landstrasse/Mitte, Rennweg and Hauptbahnhof as well now. In fact, the area around Westbahnhof is pretty seedy and should be avoided (safe, but yucky).

When we were in Salzburg in 2015, we got a room at JUFA Hotel. It is a casual hotel, with lots of families just slightly higher quality than a hostel. It is close to the old-town area. Breakfast was fine, with a lot of traffic in a large room.

We stayed at Pension Katrin in Salzburg last month. Sandra was a wonderful host, breakfast was fantastic, and we liked the location. It's a 2 minute walk to a stop for the #5 bus line and about 20-30 minutes to old town. The double rooms in the off season (which looks to be when you are visiting) are at the higher end of your budget, but I think it's worth your consideration!
http://members.aon.at/pensionkatrin.at/PreiseNEU-E.htm

In 2012 we stayed at Neutor hotel Salzburg Zentrum. It was adequate and had a nice included breakfast. A short walk through the tunnel and you’re in the main center of the city. The hotel looked like it was out of the 1970s and could have used some updates, but was fine for the night we were there.

IN Vienna, I highly recommend Hotel Austria. Small hotel, great people, elegant, fabulous buffet breakfast included in room rate.
In Salzburg, we had a lovely stay at the Hotel Hohenstauffen. It was quite reasonable, very close to the train station. It is a small inn and the people were very nice. It too had a large breakfast selection included in the room rate. It is about a 15 minute walk mostly along the river to the old town which we didn't mind at all.