Advice Best Hotels/Pensions/B&Bs for First-Time Vienna Visitors?

My wife and I, in our early to mid 60s, are planning our first trip to Vienna this coming September. We're looking for recommendations on where to stay. We're interested in comfortable, clean accommodations that offer a good location for exploring the city. Hotels, pensions, or B&Bs are all options we're considering. We'd love to hear about your experiences or any hidden gems you've discovered in Vienna. Any advice on areas to stay in or places to avoid would also be greatly appreciated.