I would find out how the ancient Egyptian pyramids were built, observing the logistics involved in transporting such large-scale blocks. Then once the 1st tier was built, how did they lift the next set of blocks to the 2nd tier etc?
That's unlikely to be surprising, since we know how it could have been done with the knowledge and technology and (most importantly) manpower we know they had. That's almost certainly how they did it.
If you wanted to "lift" very heavy stones in those days, you didn't lift the stones. You raised the ground level by building a solid ramp of packed earth or sand. People can haul a 40 tonne weight up a 7% incline. People can build a solid ramp as high as is required. You just need enough people. We're used to thinking of building in terms of machinery. Doing it without machinery requires a different way of approaching the problem and a lot more people.
The only unknown is the great pyramid because its height rules out a straight ramp to the higher levels. With the low limit on the incline, the ramp would have to be implausibly long and large. Having said that, almost all of that pyramid (or any pyramid) is in the lower levels (which could have been built with the traditional ramp method).
I'd be more interested in using time travel to find out why things were built than how they were built. No need for that with the pyramids, but Stonehenge would be a good candidate for that. More accurately, the henge before it was stone. The stone construction was probably built for the same reason as the earlier constructions there.
I'd also like to find out what Caesar's plans were - did he intend to restore the republic?
Hitler - did he really believe the crap he was spouting or was it all about getting power?
Of course, finding out the reasons for things would be a problem if you couldn't interact with the past in any way.
Overall, though, I'd want the technology to not exist. It would completely end all privacy because even a nanosecond ago is the past.