Here's another retired librarian to add to the mix. I'm not a super-geek, but I went over to the digital dark side professionally long before I retired (11 years ago).
My husband and I are r-e-a-l-l-y slow travelers. Every day has downtime, partly because he is a late sleeper and I'm an early riser. He has been known to sleep past the hotel breakfast on more than one occasion.
We are usually gone at least a month and never feel at a loss for what to do. What others have said about easing out sounds just like us. I am always amused at the things people say they would never do in Europe because they would take away from the time they have for sightseeing or somehow diminish the experience in some way. For us most of those things teach us more about the country and culture than some of the sights we see. From my perspective, that's because most of the sights we see are about the history and past culture of the country, not necessarily what it is now.
When I was on my first trip to Europe in the 70's, I met an Australian at a hostel who said she only went to one major thing each day. I took that to heart and have tried to travel that way ever since. That would probably drive most people crazy. We fully expect that we won't be able to do all the things on our lists, that events might intervene and that we might have to alter our plans. Those last minute changes usually add a little spark to the experience.
My husband's penchant for taking pounds of books ended in 2012 when I got him his iPad. I started taking my Kindle in 2012, but now only take my smartphone and use it for everything, including taking pictures. We load the iPad and my phone up with books before we go. (I love you, Amazon Prime). We never finish all of them before we return.
We are able to use Wi-Fi for all the written communication. We use Verizon global access for our phones. We don't use the data due to the exorbitant cost, but we find the phone call and texting costs very reasonable compared to the overall cost of our trips.
I read before I go to sleep every night, no matter where I am. I love using my smartphone for that. Paperbacks and the Kindle are too heavy to use to read in bed as well as to put in the luggage.
I love watching TV in other countries (except maybe Spain after midnight). I feel like I learn a lot about the culture that way, even if I don't understand the language. There's CNN or BBC in most places and sometimes we even have access to English-language, or at least sub-titled movies.
We have yet to go to a movie in Europe on a trip together. I did go to a movie in Heraklion in the 70's. It was in English with Greek subtitles. It took awhile for me to realize that I was the only female there. I was glad that I was with a male traveler at the time. That definitely taught me something about the culture, at least 35+ years ago. I also went to a movie in Brussels in the 80's. It was in English with Flemish subtitles. It was the first time I had ever been to a movie that showed advertising. That's common in movie theaters here now, but it was unheard of back then.
Going to the theater in London is just the best, and I'm so glad we went to an evensong service at Westminster Abbey when we were there. I don't know if those experiences would count as downtime or wastes of time for some, but they were highlights for us.
Downtime for us is so positive, I guess we don't even think of it as a challenge. It's a lot of what we do on our trips because we like just being there.