We've got three kids (currently 15, 12, and 5) and we've traveled internationally with them since the little one was only 8 months old. In fact, when she was 14 months old we did move to central Europe, where we still live now, and so our transatlantic flights now serve to visit friends and family in the U.S.
So I've traveled (by train, plane, and automobile!) with kids of all ages and agree with a lot of the advice already given: think about a slower pace of travel, and try to plan having a "home base" (hostel, hotel, etc.) most days. Kids get cranky and need their rest and it's good to have a place to retreat to during the day and not just at night. For budget travel, there can be nice hostel or B&B options that are kid-friendly and not expensive. Hostels can be great for storing and preparing your own food, too, which can keep a picky eater happy and save money.
I've never been one for organized tours and prefer what you could almost call "untravel" (like people talk about "unschooling" their kids). That is, I go to a new place and plan to just settle in for a few days and experience what offers itself to me without setting a lot of goals or making a lot of advance plans. Usually a particular place has certain attractions that everyone visits (some of them worthwhile and others not), but these are usually easy to accomplish without advance planning unless we're talking the Eiffel Tower during high season or something. Otherwise simply walking around, checking out the local grocery stores, and soaking up the atmosphere usually leads to serrendipitous and wonderful discoveries that wouldn't happen if you were being marched from one blockbuster destination to the next.
Our visit to Helsinki when the eldest was a baby was a work trip -- husband went for a conference -- and I spent the five days basically blissfully hanging out there, discovering that public transport was free for both me and her (because she was under six) and finding that Helsinki was just full of wonderful little parks where we could stop and have fun. Some of the cool surprises that just happened: meeting a live reindeer in the street with a handler who was letting children pet it and sit on it; seeing a parade celebrating the end of WWII; striking up conversations with several shy Finns who couldn't resist talking to my adorable baby; and taking our pictures by an actual stuffed polar bear in a downtown department store (impressively tall and fierce!). We also took the ferry over to Tallinn for the day just to visit another country but without any particular expectations of what we would do there. It was a relaxing stroll through the old town that offered lots of views and experiences without needing anyone to guide us. I came home feeling refreshed and rested but also with a head full of new impressions of Finns and Helsinki, so I don't feel I missed out on anything. And my daughter was happy and content the whole time, too, including on the flights.
What are you particularly looking forward to seeing/experiencing? We've done lots of travel around Europe, most of it with kids, and I could make some suggestions based on your interests.