I'm a great believer in travel expanding the mind, We took our children out of school on a couple of occasions and marched them around cultural places, amid loads of moaning and groaning. I was always having to visit castles, battlefields, cathedrals as a child with my parents, being bored to tears, I'd say to mine at the time, "you'll appreciate all this one day", and that has been the case, often it's in retrospect, as it was for me, they have told me as adults, "can't believe I was bored when we were at such and such a place"
I think there is a great example of just how much travel can have an uplifting effect on a young person, anyone who has seen the first "Race Across the World" might remember father and son, son aged 17 in the first leg whining quite a bit and coming out with classics such as "I'm having a breakdown, I'm missing my XBox" by the time they'd reached the final destination having travelled through some truly amazing places, rising to challenges, embracing and admiring cultural differences, he'd turned into, to all intents and purposes a fully fledged adult.
I feel somewhat cheated if I don't see something of the country I'm visiting, I met some tourists in Mexico who just wanted the beach, amazing as the beaches are there, the ancient sites and flora and fauna are far too unique to miss. Having said all that, last summer it was particularly hot when we went to a beach resort on the Spain/Portugal border, I found myself just wanting to lie by the pool, swim and read, having previously done a couple of week long city breaks in Seville and Cordoba, Granada as well as Lisbon on a separate occasions in cooler months. These days I find heat strength sapping so I don't feel like doing a culture trail, but that's not because I'm not interested in the country in question.