Whatever I feel like on a given day. I hate itineraries. I like going on vacation with a general idea of what I can do, and then picking and choosing when I get there.
That's difficult to say, because it's entirely dependent on the destination.
I like both urban and scenic exploration. I have trouble sitting around, unless my body needs the rest. So, I stray away from most "leisure" activities. Sitting on the beach for hours is not for me. If the destination has a high walkability factor, I will walk everywhere I physically can, and I will do it A LOT.
I barely take any pictures. I find that they detract from my being in the moment, and they never capture what I hope.
I do like thrifting for niche, often older electronics and peripherals.
I like food.
I like cigars, and love cigar bars, because the atmosphere and activity is excellent for meeting locals and travellers alike. That is one thing I will always scout out and do.
I went to Osaka, Japan earlier this year. I returned with 2 large suitcases packed full of retro video game consoles and peripherals. Their LaserDisc stores were insane and floor to ceiling with stacks of discs. I so badly wanted to pick through them, but LaserDiscs are notoriously heavy, and I couldn't spare the luggage weight.
A few years back I spent a year living on the road, all across the US. I brought back a huge haul that time, notable acquisitions being an Atari Jaguar and an NEC PC Engine.
Respectfully, I'm assuming a "vacation" here is a US-ism for what we in the UK would call a "holiday" (i.e. a recreational trip somewhere), I'm not sure if there are nuanced differences. To see as much as possible of the local culture is generally my aim, that's my main reason for travelling. I'm not saying that in a snooty "high culture" way at all, sometimes the most mundane cultural things can be the most interesting. Also to try the local cuisine. I like trains, so going to places I can explore by train are great - Interrailing around Europe have been some of my favourite trips. Also I did a great train trip around Japan pre-covid.
I think we (Americans) likely use "vacation" almost synonymous as you would "holiday", with little-to-no nuances. We probably distinguish them from the term "holiday" because we culturally define "holidays" as various annual observances, religious or federal.
Nothing, anything? I don't actively plan for vacation except maybe where I'm gonna be. Once there, even if I am in another city, I go with the mood of the time and try not to feel obligated to do anything. If I stay home sometimes I end up doing things that were put off for a long time, I finish them, grab a beer meanwhile, afterwards, even if it's in the morning as long as it's hot and that's it for the day.
I have a rough outline of things I'd like to see. Such as some tourist attractions , nature sites , zoos , museums etc.
We do as many as we can but also eat out along the way. We avail of metro , trains and walking where possible. If the city has a river or canal tour we usually do that too.
Mainly it is just to unwind and get away from the rat race for a few days.
Depends on where I'm going, whether I've been there before, and how long my trip is, but as a rule I'll always seek out the local food and try to see a mix of famous big-name sights and weird niche things that interest me. For example, when I was in Tokyo last, I went to the top of Tokyo Tower at sunset (normal tourist sightseeing thing) and also went to see their underground flood-control tunnels.
I don't enjoy "sit on a beach and do nothing" vacations, but more power to you if that's your style.