My wife and I are big believers in family vacations and therefore we started made it a tradition that we go on a family vacation every year possible. We live in the greater Kansas City area, so when our kids were ages two and four, our first vacation was a one week trip to St. Louis, which is just a 4 hour drive for us. We went to the basic tourist type places such as the Zoo and to see the Arch. At those ages, the kids also just enjoyed the simple things such as staying in a hotel and swimming in the pool every night. Even though they were very young during the first years of our family vacations, they still understood that a week on vacation was a different routine than usual and that we got to spend the whole week together as a family.
The next year we tried a longer driving trip to Texas and frankly we were not sure how the kids would do with the longer drive time, but they did pretty well overall. I would recommend doing something along these lines where you start off with shorter driving vacations when your kids are younger, then increase the distance, and just see how it works for your family. The following year our kids were ages 4 and 6 and they had done so well on the longer driving vacation that we felt comfortable taking them on their first airline flight. We flew to California and of course we visited Disneyland, which was great (you would almost have to be doing something wrong to not have a good time taking your young children to Disneyland).
From there we mixed up our vacations, sometimes driving and sometimes flying. We generally tried to go to different destinations, such as South Dakota, Florida (Disney World of course), Colorado, Wyoming, just to name a few. We stayed in the Continental Unites states until they were ages 9 and 11 when we went to Hawaii. We took them on their first international trip when they were ages 13 and 15 and they seemed to be mature enough at those ages to really appreciate the magnitude of the trip, as traveling internationally is a much bigger deal both in terms of costs and travel times.
As time has gone by and our children became teenagers and now have become adults, trying to plan family vacations naturally becomes more complicated, as the kids now have schedules, whereas when they were young we could just do what worked for my wife and I. Therefore I highly recommend starting your family vacations as early as possible.