DON'T assume you will be back, unless you really prefer returning to familiar places. The world is HUGE with so much to see, and you never know if you will get another chance. Travel is also expensive, so, unless you are independently wealthy, make the most of your money and get out there. When we were in Paris, we stayed in an apartment 2 blocks away from Notre Dame. The first day, we went by it, saw the lineup, and decided to leave it for another day. Nearly every day, we passed Notre Dame on the way to/from our apartment, promising ourselves that we would go inside at some point. Well, we never did. And since then, Notre Dame had that destructive fire, so even if we do ever get back to Paris, seeing Notre Dame likely won't be the same. So, now my husband and I have a saying: "Don't let this be another Notre Dame," and we try not to pass up opportunities to see things. That is not to say that we try to see everything, but that if we want to see something, we would never leave it for "next time," because who knows?
That said, DO try to zig when everyone else zags. Travel during shoulder season, if possible. See popular sights early in the morning or late in the day.
DO poke around corners and go through gates (public ones) to see what's there. Don't always follow the crowd.
DO see things through the lens of your camera if you like taking pictures, as I do. I find that I see differently when I am looking for interesting photos to take. I notice details more. I notice the flora and fauna, as well as the castles and mountains. I see things others walk right by. I see a couple, him wearing a beret, being romantic outside the greenhouse of the Jardin des Plantes in Paris. I see children chasing huge bubbles in the sunshine outside St. Stephen's Basilica in Budapest and chasing pigeons through puddles in Plaça de Catalunya in Barcelona. I see the Peruvian Hairless Dog dressed in a fuzzy vest in Aguas Calientes. I see funny details on doors. And I have photos of all these things to remember them. My husband and I go through our photos nearly every evening before bedtime when we're travelling, and he often remarks, "I didn't notice that," when he sees my pictures. He now takes more photos of his own and sometimes captures a moment that I missed! Also, no matter how busy our days, they are never a blur, because we have our photos.
DO go into that 14th cathedral of your trip. A number of times, my DH and I almost didn't go into yet another cathedral, because we had already seen so many. And every single time, when we decided to go in anyway, we were so glad we didn't miss it. Every one has something different and special about it. But, perhaps, realizing that comes with noticing details.
I completely agree with learning a few words in the local language. I always learn "hello" (or, more likely, "good morning", "good afternoon", and "good evening"), "goodbye", "please", and "thank you", at a minimum.
I agree that comfort is more important than fashion.
I agree with packing light.
I agree with doing what matters to YOU and not to everyone else. If sitting in a cafe for hours appeals to you, do that. If it doesn't, don't bother. It's YOUR trip and YOUR money. To thine own self be true.