Depends on if you want domestic or international and how long the trip will be, your budget and what your daughter's interests are. To answer the initial question as to what my personal most memorable vacation was I have a few.
When I was a teenager in the 70s Daddy had 6 weeks vacation, 4 of the six of us kids and my parents piled into the family VW van and went from Albuquerque where we lived across to southern California and up the coast, back down through Nevada on the way home. We camped the entire trip. This was when you could pitch a tent anywhere, literally on the side of the road if you wanted. We had a big two room tent that Mama, Daddy, one of my brother's and myself slept in and my two oldest brother's had little pup tents they pitched beside us. We camped in the dessert, on the beach and in a few state parks.
When I graduated high school all my brother's had moved out and Mama and Daddy lived in Saudi Arabia. I lived there a while then came back to finish out high school. I went back over there and we went from there to Rome for 4 nights, then to Switzerland where we rented a car and drove all around the country for a month. We had no reservations anywhere except the hotel in Rome and the initial hotel in Switzerland. Otherwise we had no destinations in mind, just took off and went where the road took up, stopping wherever we thought it was interesting. Sometimes just for a night, sometimes for a two or three. We were actually supposed to stay a week longer than we did but you can't go from the dessert to all those flowers and cooler weather and last for more than a month. It was in August but there was snow on lots of the peaks of the mountains.
Hubby and I are scuba divers (not so much now that we have a dog and aren't spring chickens) and we took a once in a life time dive trip to Palau. We were on a live aboard (think bare bones cruise for divers) that was a small yacht that held maybe 15 passengers then maybe 7 crew. We got the sort of penthouse cabin which had it's own balcony and more room than a normal dive boat room. Great diving, great crew and boat. We stayed an additional two days after the week long dive trip and one of our dive masters took us all around the island and showed up non tourist spots. Best dive trip we have ever had.