I agree, Vienna is exceptionally nice and definitely worth spending a few days. You could also consider taking a train to Salzburg and to Innsbruck, again both delightful towns and easy on the feet, especially Innsbruck which is compact and has excellent public transport and great views from the mountains both North and South of the town (the access to those mountains is included in the "Innsbruck Card"). The train trip from Vienna to these two towns is also very nice, you can relax and enjoy the scenery.