I’d set the machine for exactly 100 years ago, to try to get some clue to who or what is imposing that restriction, why, and how. Similarly, I’d set the location as high up as I can get it before running afoul of the “not off the Earth” restriction.
I’m a lot less interested in the past than in this wondrous technology for viewing the past.
I’m sure there will be other people doing this kind of thing, but I’d volunteer to assist Príncipe de Viana (my local historical society) in obtaining recordings of Joaquín Gayarre’s singing.
Also of different Basque dialects. Basque has this issue where it used to be written very little (reasons below) and when it started getting written in high volume it hit a prescriptionist storm. So information on pre-prescriptivism dialects would be interesting both for personal reasons and to anybody who is more interested in the history and mechanisms of language than in its politics.
Reasons: most speakers have been multilingual for the last two thousand years or so. The first “other language” would be the local language of government, so government stuff or stuff the government might be interested in would be written in it (well, that the government might find of interest and you didn’t mind…). And when writing to someone in a distant location and unless you were sure they spoke your own dialect, again that other language would be more useful. So for the longest time it was only private records that were written in Basque.
I’d quite like to see how much earlier generations of my family lived - many farm labourers, no doubt, some devout members of minor Presbyterian sects in Scotland, some Victorian soldiers, and one family in particular, the product of mixed race relationships in 18th century Jamaica, so some slave-owners and some slaves - what was their life like, how could they manage such seemingly frequent trips back and forth between Jamaica and London?
And for historical interest, the English Civil War period.
It turns out Harold is not actually dead - he is seen speaking with an embroidered figure of Samuel L Jackson, who is wearing an eyepatch.
I’d do a lot of research into certain Old Testament Bible stories to see if they really happened or if they simply serve as a mythological basis for the origin of the modern-day Hebrew people (I suspect the latter is true. I have far less difficulty believing the New Testament). Adam and Eve, Noah’s ark, Sodom & Gomorrah, Jacob’s ladder, Joseph in Egypt, the Exodus.
If this was the basis for one of those old-timey sci-fi stories, the whole thing would end up with bad consequences. Like the only people in the future who dare have any sort of historical significance are the absolutely shameless nutjobs.
Just give me a couple of days to take pictures of manuscripts at the Library of Alexandria. Doesn’t matter that I can’t touch them, I can take pictures while the people are looking at them.
When I was a child, in front of my great grandfather’s house (that he built), was an old, broken down and tattered horse drawn wagon.
My grandfather told me that was the wagon my great grandfather and his wife moved to Texas in. Built the house in the middle of 600 acres and raised cattle.
Being able to see and touch that wagon really captured my imagination as a young boy.
I’d like to witness my great grandfather and his wife make that adventure into Texas.
How messed up would it be if it just so happens that the only books popular enough for anyone to want to read while you were there happened to be the books we still have? Like, you could be looking at Homer’s lost writings right there on the shelf or something, and people keep grabbing the Iliad. :mad:
My great-great-grandparents lost six of their children to cholera or diptheria over Christmas, 1871. No one really knows what happened.
It would be horribly difficult to see, and not being able to do anything like bring pockets full of penicillin (if that would even help) would make me feel helpless, but I’ve always wondered what those poor kids died of, and how the family was living back then. I know it was in a small shack by a branch of the Chicago River, so I’m guessing it was damp and nasty, but I’d like to see it.
100 years from now? 9 October 1916 and watch Babe Ruth start Game 2 of the World Series.
Otherwise, I’d wait until 2028 so I can find out who my maternal grandfather was. All we have is a name on a birth certificate.
I like that plan. That’s a project that would benefit from many people using their turn to contribute to the data set. I bet there would be hundreds of groups pushing for crowd-scanning projects like this.
The language projects are also cool. I’d be interested in scanning languages in North America before European contact. I’m sure I’d be able to hook up with an existing crowd-scanning project that could assign me a useful time and location.
What really happened to Natalie Wood, but I imagine her surviving family would have beaten me to the punch, as it were.
Again assuming people hadn’t gotten to it first, time lapse of the creation of the Great Lakes, assuming my time machine has access to a good angle from the atmosphere (depending on the OP’s meaning of not moving away from Earth). Or other cool, geological features for that matter.
This makes me want to Dance With Myself!
If all the obvious stuff has been captured, I’d probably go to England in 1633 and try to figure out what my ancestors had against the Virginia colony that made them decide to settle in the frigid northeast instead when they traveled to the US.
I want to watch what unfolded when Moses sequestered himself on the top of a mountain.
I don’t believe for a moment that a burning bush carved out 10 ( or 15… 
) Commandments. I believe that this complex fellow realized he needed to UNIFY things, because they were just going to shit down in the valley.
I also very much want to witness the moment- and there must be A MOMENT- when Cuneiform was tried and accepted between two people as a comprehensible form of communication.
On a personal level, I want to see the day my ancestors first entered Germany from wherever it was they were coming from. ( The Nazis very neatly demolished all family history so there’s no knowing where my people came from. )
Me, I’d like to view the Burgess Fauna and pre-Imperial Japan…
Okay, just so I’m clear, we can’t use this thing to go forward to the future at all? 
That was my first thought. Personally I’d go for the premiere of one of the Mozart operas or maybe Beethoven 9 (which was, shall we say, not overly successful), but if we’re recording it might be fun to grab the 1913 premiere of Rite of Spring, just to see how bad the riot really was and what prompted it.
So would you say that was a misconception on his part?