Hello again. I did a search to see what is available on booking.com (no affiliation) for your dates and within your budget. Here are my recommendations:
My top recommendation is the Austria Trend Hotel Savoyen - a great location on Rennweg adjacent to the Belvedere and a 5-10 minute walk (2 minute ride on tram 71) to the Ring. My family has stayed here many times. It is an elegant hotel with larger rooms and a good breakfast.
The rest of the hotels I am finding are either 1) modern; 2) in an inconvenient location; 3) or both. Of these, my top would be the Hotel Indigo, an exceptionally modern building sandwiched between old beauties in the 5th. The location is directly in front of the U4, which will whisk you to the center in about 5 minutes. Additionally, that neighborhood is fantastic. I has posted previously that some of my favorite restaurants in the city are nearly (Silberwirt, for example). Work colleagues stay here every time they visit and they are very pleased (plus as an IHG property you can earn points).
If I had to choose a third, I would go with the Holiday Inn Vienna City, also in the 5th district and also nearby my favorite spots (I'll give you another one - Propeller). This is a reliable, modern hotel in a very good location.
As you might have noticed, many hotels suggested above are likely unavailable or out of budget due to the prime time in December you will visit. That said, I think all three of these are really fantastic choices.
