Vienna: With a rental car, stay inside or outside the city?

As part of our driving tour around Austria and Hungary next spring, we are planning on spending several days in Vienna. We've been there several times before, but never with a rental car. We certainly wouldn't need to use the car while there since public transportation is so good, so long-term parking is a concern. We are debating possibly staying in a smaller town outside Vienna to avoid the hassle of driving and parking in the city, and this could also potentially give easier access to biking routes along the Donau. We are wondering which is the best approach to take. Any recommendations or suggestions from anyone? Thanks! KateN.