Quick food tip given you have a 6 and a 10 year old. There's a (global) chain of quick-service Italian food places called Vapiano with 4 or 5 locations in Vienna. You pick up an RFID card on the way in, order at different food stations (pasta, pizzas, entree-size salads, the bar, etc) where they charge the RFIC and give you a pick up buzzer, find a table in the stylish/casual interior, then hand your RFID to the cashier and pay on the way out. The food is easily passable for adults and our little kid was in heaven. Quite affordable and large portions easily split between two. Not for every meal of course, but I think we did a lunch and dinner in 4 night in Vienna when we wanted quick meal without much ceremony that was sure to make our little one happy.
Also kid-wise if you're going to Vienna in the summer when the weather is warm there are a couple of fun things for them to do on the long island in the middle of the Danube. Very close to the U-bahn (maybe S-bahn? I forget) stop on the island is a good-sized "natural" water play area for children - series of connected artificial (but naturally set) wading pond and beaches for children. There fountains to play in and a Huck Finn style raft they can pull back and forth across the largest pond.
Also farther out on the island is a large pool complex called Gansehaufel - there are several large swimming pools, a wave pool, a water slide, a play-structure set in water, acres and acres of lawn to play on, a nudist area behind a fence for privacy, lots of Danube beach-front, snack-bar, scores of communist-looking A-frame locker rooms. My 7 year old daughter had a blast there for a couple of hours as reward for behaving so well in all the museums and churches, and I enjoyed it too - enough to call it a cultural experience seeing how ordinary Viennese live life with their families on a Sunday. It's not at all like the experience at a waterpark in the US, much more of trip to the park feel, much more a slower communal feel.