Why can't we observe a solar eclipse and the preceding/following lunar eclipse from the same place? Lunar and solar eclipses go in tandem so the two often happens two weeks apart.

However I noticed if there is a solar eclipse in my area then the preceding/following lunar eclipse is not visible from my area because the Moon is set when it happens.

Similarly when lunar eclipse is visible in my area, the corresponding solar eclipse is not visible at my area because the Sun is set.

Recently the same thing happens in July 2 when there were a total solar eclipse on the other side of Earth, and soon we will see a partial lunar eclipse from my area.

The only exception was when the eclipse happens near the sunrise or sunset.
For example on May 31 in 2003 a partial eclipse could be seen from Hungary at the morning when the Sun rose already partially eclipsed just few minutes before the maximum occultation.

Two weeks before that there was a total lunar eclipse where we could only see the beginning of the eclipse as the Moon was already set when totality occurred.

These eclipse pairs seem to occur almost exactly at the same time of day. 
Why?
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.