Mapping space from our milky-way to Laniakea and the CMB, we always put a star or galaxies position from the light we see in that 3d coordinates of the universe. But really if a star or galaxy we look at, is for example 1000 light years away. We are saying it is there, but in reality it's actually moved somewhere else in its orbit. So if we followed the light to a star, does this mean we wouldn't travel in a straight line? And if the galaxy was travelling away from us on earth, we would think it was 1000 light years away but we would end up travelling much further as we got closer to the original coordinates we thought we were going. Is there anyway to account for this variation? And will it ever be possible to project the real locations of stars and galaxies?
There is no 'real' location without somewhere to reference it to and or most of us the Earth is as good as anywhere.
We do need to consider the actual motions of nearby stars when we work out their position to take images, there are tables of "apparent position of nearby stars" by date.
The question of "where is it now" gets very interesting for the most distant objects. We observe them when the universe was very young and much smaller. There are many imaged objects which are now outside the observable universe - they are now far enough away from us that the light from them will never reach us, but the light we see left them when they were closer and the universe was much smaller.
This is almost a philosophical question - why limit yourself to stars and galaxies; nothing is where we see it now.
Fortunately this is not too much of a problem in astronomy because the peculiar velocities of stars and galaxies tend to be in the range of tens to thousands of km/s and so much less than the speed of light. Hence their position cannot change significantly, compared to their distance from us, whilst the light is in transit.
Nevertheless, if you wanted to navigate a spaceship accurately to a nearby star, you would certainly need to take this effect into account. A star that is 4 light years away, moving at a relative speed of 30 km/s with respect to the Sun (roughly correct for Proxima Centauri), will have moved by 25 times the Earth-Sun distance whilst light is in transit.
On cosmological scales, so-called recession velocities are not really speeds in the conventional sense; they are due to the expansion of space. A galaxy has a position/distance where we see it now, but one can also calculate (using General Relativity and a cosmological model) a "proper distance", which is where the galaxy is at the present cosmological epoch. These numbers can be very different. For example, the most distant quasars we see are around 13 billion light years away, but their proper distance is more like 30 billion light years because of the expansion of space.