I letterbox, which is like geocaching but with stamps (learn more at atlasquest.com!) so a lot of my vacation planning involves making lists of letterboxes I want to attempt. I have even gotten free trials for delivery route optimization apps before, in order to plot out the best route for the day!
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Ah, the old traveling salesman problem. That’s an interesting thought for mad-dash sightseeing.
I honestly don't know how people make reservations/plan on a phone. Its like looking through a keyhole. I might start with blogs or podcasts, but when it comes down to details I pull up a fullscreen Google Earth and fly over the destination, then start walking around the places I might stay. Second screen usually has a Google Maps with the public transport showing - or the local transport authority map. If I'm in the US I'll use https://www.smappen.com/app/ to find out how much ground I can cover on foot/by car from my rental.