Why can't we observe a solar eclipse and the preceding/following lunar eclipse from the same place?
For a solar eclipse, the Moon has to be between the Earth and Sun. For a lunar eclipse, the Earth has to be between the Moon and Sun.

Since it takes the Moon about 4 weeks to orbit the Earth, it will take it about 2 weeks to go from a lineup of Moon-Earth-Sun to a lineup of Earth-Moon-Sun.

To make this more complicated, the Earth is rotating so that it takes about 24 hours to go from midday to midday.

So, say we have a solar eclipse at midday - there's a line between the centre of the Earth, through you, the Moon and the Sun. Two weeks later, when the Moon has moved around to the other side of the Earth this means that when you go out at midday, the line is now Moon-Earth-you-Sun. So you can't see the lunar eclipse, because the Earth is now in the way.

You can see both eclipses two weeks apart when they are around sunrise/sunset because you're no longer on the line through the centre of the Earth between the Sun and Moon.

Update:

I was going to do the math - but I think that this map of eclipses in 2019 demonstrates it better. If you compare the solar eclipses with their paired lunar eclipses, we see that there is a bit of overlap (since eclipses are not instantaneous) - but since these are at the edges of the eclipse, it's practically impossible to see a full solar eclipse two weeks after seeing a full lunar eclipse from the exact same location.