My number one tip for saving on lodging for a family of 4 would be to stay outside city centres and in smaller town, whenever reasonable. For example, when we visited Rothenburg ob der Tauber the first time we stayed here it's only 5 minutes drive outside Rothenburg but we found the prices better than staying in the centre of Rothenburg. This needs to work for your style of travel and the things you want to see, though. We don't feel the need to be in the heart of the places in the evenings.
If you are choosing a place for a 'hub' stay, from which you plan to do day trips, don't be afraid to look outside the places listed in the guide books. For example: we stayed here on a trip to the Berner Oberland a few years ago (the rates have gone up since then) and paid a fraction of what we would have paid for the same accommodation in a place like Murren. The views were amazing, the community was quaint (if not guide-book worthy) and it was only a 10 minute drive (something we didn't mind) down the mountain to Interlaken.
Look for apartment rentals wherever possible. We have found some great deals for our family on those occasions when we wanted to stay in the centre of towns ... and in the countryside, too. Many places will rent for only a few days you just have to ask. This also allows you to save by being able to cook your own meals (and enjoy shopping at some of the amazing markets!!). On our last trip, we ate at restaurants/cafes/food stalls for lunch and cooked our evening meal in our apartments. It saved us a lot by the end of the trip.
Don't forget to calculate the extra cost of transportation into your accommodation prices when you stay outside a city/town centre. If you stay in the suburbs of Vienna (like we did), for example, you will end up paying for the public transportation into the city centre for everyone each day and factor that into your cost. For us, this wasn't an issue as we prefer to be in the countryside and only made two trips into Vienna over 5 days.
Lastly, don't compromise! Sometimes paying extra for the hotel in the heart of everything is the best deal.
As for your questions about itinerary, we need more information - what do you want to see, where do you want to go, etc.