Wilde from Texas, I have some exciting options for you. I looked at booking.com and considered your budget, dates and overall location (as well as any personal experiences I have).
Here are seven suggestions:
Small Luxury Hotel Altstadt Vienna - a really sweet hotel in the exceptionally desirable 7th district of Vienna. Right next to probably the most beautiful church square in Vienna (which also includes the fabulous Erich and Ulrich restaurants), this hotel is very close to Spittelberg the best Christmas market in Vienna.
Singerstrasse 21-25 Aparthotel - I actually stayed here for a month when I moved to Vienna. The location couldn't be better (just look at Google). This room has a small kitchenette, which might be nice. Modern and high quality.
Imperial Riding School, Autograph Collection - I have had guests stay here more times than I can count. The hotel recently underwent an huge renovation and the look is modern in a historical building. Breakfast is fantastic. Also an indoor swimming pool which is rare. Location is great, right next to Rennweg, so easy access to the S7 airport train and the markets of Karlsplatz (the other best market) and Belvedere.
Boutique Hotel Das Tigra - I am recommending this hotel because of the location. It is prime. Sandwiched between the third best markets of Freyung/Am Hof, you are right in the heart of the action.
Hotel Kaiserin Elisabeth - Also, again, recommending this quaint hotel based on location and reviews. Really great choice I think.
Hotel Gilbert - This is a newer hotel, but very popular. It is squeezed between the funky market at the MuseumsQuartier (MQ) and the uber-fabulous Spittelberg. I think this is a great choice too.
Austria Trend Hotel Savoyen Vienna - I have had guests stay here many times. Modern rooms, great breakfast, classic facade. Walking distance to the Ring, Belvedere in the backyard, Karlsplatz market just down the street. S7 airport train one block away.
I hope this helps!