Today is the last day of my Nasu trip. My friend and I went to Nasu Highland Park, which is an amusement park. It’s the largest park in Tochigi, with around 40 attractions, including thrilling roller coasters. I have fully enjoyed myself on/during our trip.
This sentence (below) means the trip is over. But according to your first sentence (today is the last day...) it is not over.
It was the first time I’d traveled with my friend. It was a really good memorable trip.
So you need to change your tenses:
This is the first time I've traveled with my friend. It has been a really good memorable trip.