1. Cruises - The European cruise market is becoming busier and busier every summer. A cruise offers a lot of options for parents with young kids. Your family gets the chance to visit a number of European cities while sleeping in the same environment every night. You can choose to return to the ship for a dinner of foods your children recognize. The cruise ships also have children's programs included in the fare that create the opportunity for you to get some alone time with your significant other.
2. Escorted Tours - Adventures by Disney offers specially crafted itineraries and activities for families with children. One benefit of an escorted tour is you are sure to see the highlights of key areas with the benefit of a tour guide. When searching for an escorted tour for your family, it's important to pay attention to how long you'll be in transit each day and making sure you have some free time in each city to explore at your own pace. Many tour use bus tours to explore cities and the countryside, this could be challenging depending on your children's ages.
3. On your own - Crafting a unique agenda for your family may be the best way to explore a European county. You could choose to rent an apartment walking distance from some of the neighborhoods you want to explore. This provides a homey environment as home base. You could choose a US branded hotel that looks and feels a bit more like the USA. You could choose a local inn, castle, or bed and breakfast that offers an immersion experience.
Travel agents provide a great benefit in helping you sort though all these options and finding the best fit for your family.