My husband and I tend to be early starters when we have the option. Back in the days when we had to drive to Florida to see his parents, we’d be on the road in the dark of the morning, and do the same for the return trip.
Eons ago when our daughter was a toddler and we were lots younger and still working, we’d sometimes head out at sunset to drive thru the night in the hopes that the kid would sleep for most of the trip. That’s now my daughter’s preference, not out of nostalgia, but because they have 2 kids and SIL has insomnia, so he likes to drive overnight.
On the rare occasions that we fly, we try to time our departures/arrivals to avoid driving in rush hour traffic, but that’s not always an option. We’ve never traveled by train - I expect it would involve the avoidance of rush hour as well.
We have house guests who will be leaving tomorrow. I asked when they thought they’d head out. The answer was “whenever” I dunno - some people…
As early as possible. I have lots of energy in the morning, and it wanes as the day progresses. I want to be as sharp as I can be when I’m driving, so the earlier, within reason, the better.
Never overnight. Often pre-dawn. Avoidance of rush hour matters a lot, whether at either end or along the way.
Of course, I’m naturally an early riser; today I was out of bed a few minutes before 0500. When dealing with a co-traveler for whom “the crack of noon” is a serious comment, not a joke, well … getting underway happens much later after far more folderol.
We tend to be early risers. I get up at 6 am, and my wife often wakes earlier. Our most regular long drive is Chicago to Denver. We often try to get on the road around 4am. Being around Chicago, an early start helps avoid any traffic issues starting off.
We have loads of kids including one with special needs who travels with a lot of medical equipment. So while we will typically have the stated aim to get off “before lunch” we will usually be lucky to leave the house before dinner
I live in England, but have visited friends in Las Vegas several times.
(So this is a plane flight, not a car drive.)
I book a flight for late morning, then travel down the afternoon of the day before.
I check my bags at the airport in the evening (no queues and you can sometimes get a seat upgrade - because they know then how full the plane is.)
I stay overnight in an airport hotel (it costs a bit, but I’m avoiding any rush or risk of arriving late!)
Next morning a leisurely breakfast followed by a courtesy bus to the airport, a stroll past the queues of screaming kids and panicky adults and just wait in the departure lounge.
I usually hit the road between 10 and noon, earlier if I want to be someplace right when it opens. I like to end up the day with time to wander around a bit before dinner. When I was working I’d leave for vacations right after work or super early the first morning to squeeze every minute out of my time off, it was actually a bit stressful. Now the whole process is much more relaxed. Sometimes I don’t even make my first night’s reservation until after I get up in the morning.
My Dad always wanted to leave for our family vacations in the middle of the night. Most of our stuff was loaded into the car the day before, with the coolers, assorted food, and us kids put into the care just before we took off. Dad had slept as much as he could during the day so he could drive, and some of us slept during the early part of the trip until Dad decided it was time to stop for breakfast.
Early enough to beat rush hour in the next major city. If I’m leaving Milwaukee and heading South, I want to be on the far side of Chicago by 6am, so I’d leave sometime between 4 and 5 am.
It’s been a long time since I’ve been on a road trip, and the last time I drove any significant distance at all was due to a scheduled necessity (the funeral of my best friend ) which was only about 100 miles or so.
Otherwise the only real road trips I’ve taken in recent memory have been to either cottage country in northern Ontario or wilderness parks, also in northern Ontario, in both cases a drive of several hundred miles. My guideline is to always leave early enough to arrive while there is still daylight.
An aside. At one of the lakeside cottages we rented once, there was a furious thunderstorm on our last night there, and the power went out. We were supposed to leave the next day anyway, so we figured we may as well leave right now. Everyone and the dog piled into the van, and when I started it I realized it was very low on gas, and with the power outage the local village would likely not have an operating gas station, and would probably be closed even if they did have power. So with the thunderstorm still raging, off we went into the darkness. It was like a scene from a horror movie.
Epilogue: we made it to civilization and a 24-hour gas station. Judging by how much gas it took to fill up, there was very little left in the tank! The only passenger not the least bit worried was the dog.
Neither of us is diurnal, and I actively prefer driving in the night. So we tend to get on the road around 1 PM. Often drive until 2 or 3 AM, as long as the motels will let us in that late, or we have another destination (e.g. home).
We prefer to get a good night’s sleep, so not too early, and rush hour means we don’t want to leave before 9. Going to Seattle to see our kid takes two days at our age, so getting to the hotel halfway early doesn’t really offer an advantage.
I know this is about car travel, but we prefer the earliest flight possible, which means a Lyft pickup at 4 am or so. I reserve it, and it’s never been a problem since it is far enough to the airport to make the gig worth it for the driver.
I drive from Chicago to Green Bay every few weeks, to visit my elderly parents and help out with them for a few days.
When I drive up, I shoot for getting on the road around 9:30am, so that I’m past the peak of rush hour here in Chicago. When I come back home, I try to get on the road south between 4pm and 5pm – I typically stop for a bite to eat before I get to Milwaukee, and that timing gets me through both Milwaukee and Chicago after evening rush, but before it’s late in the evening.
Why I mentioned getting to the airport. However your freedom to select a start time is severely constrained if you have a plane to catch and security to go through. One of the reasons we like driving is that we get to choose when to leave, which is never 4 am.
My preference is to leave around 4am, and be far away from familiar stuff by the time the sun comes up. However, I did do a glorious road trip once with a couple of friends. We left Los Angeles at 10pm or so, drove all the way up the California coast on PCH, arriving in Big Sur about the time the sun was coming up, then having breakfast in Monterey. It was a spur of the moment thing, with no prep, and it remains one of my favorite road trips of all time, even if it was dark the majority of the way.
I am not one of nature’s early birds. I’m not leaving until I’m ready, which means having woken up, had coffee and finished packing- normally between 9 and 10 is about the earliest I’m ready to go for a trip, unless it’s a flight or something.
I once had a job cleaning holiday cottages in Cornwall, England. Checkout time was 10am, check-in was from 1pm. We had one family show up at about 9am because they’d left London at about 4am ‘to beat the traffic’, with a car load of extremely grumpy tired kids. They didn’t seem to understand that they couldn’t just get into the cottage and go to bed as soon as they arrived and got really annoyed at us for not being all impressed at their organisation skills and having the place ready to go.
Whenever you decide to leave on a trip, just don’t do that…
At least not without pre-arranging things at the destination hotel. As a career traveler, I’ve checked in, or out, at each of the 24 hours of the day. And had a room ready for me. It just takes prior planning.
Folks who rarely vacation don’t realize all the stuff they don’t know. Which often bites them.
I dunno - some people… 
and just wait in the departure lounge.
) which was only about 100 miles or so.