Welcome to travel blog. It looks like you have a fantastic trip planned for the up coming months. You've posted a good question and hopefully you will receive many interesting answers.
Holland, Belguim, France, Italy, and the UK for three months will be wonderful.
I will steer my answer to the locations you will be heading to on this trip. Plus I will recommend things that don't cost much money.
We like to get up early and sit outside at a cafe and people watch. It is wonderful watching a city come alive in the wee hours.
When in Belgium and France it is recommended to sample the chocolate. We were on a mission to decide which country had the best. We were not able to come to a conclusion so we will continue our research on the next trip to those locations.
Nothing better than sitting in a pub in London and getting involved in a political conversations. Many English have strong opinions and are more than willing to share them. Take a bus and sit at Stonehenge for a couple of hours.
We enjoyed being in the first car heading to the top of the Eiffel tower. However, I have been told it is lovely at night.
Cafe Marley in Paris is across from the Louvre. We sat outside with a bottle of wine and a plate of cheese and watched the sunset and the lights in the fountains come on.
Climb to the top of every church you can as the views are always great.
Sit quietly in every church to enjoy the serenity.
Find music in every city as music is the soul of the town. Street performers or in formal establishments increase the understanding of the people.
Talk to as many strangers as will talk to you. For us traveling is about the people and better understanding their daily life.
Learn about life in each town.
Bayeux is a lovely town in France and one of our favorites.
San Gimignano is one of our favorite Italian towns and we enjoyed the island of Elba. We are water people so we always enjoy taking a ferry to an island.
In Holland we liked Delft and everyone loves Amsterdam. It is alive!
That should get you started.