most of the astronomy images we find online have some color modification
How close to the false color images would they be
This is a common misconception, that the pictures you see of galaxies and nebulae are necessarily "false color", "modified color", or "photoshopped". Some of them, yes. But a lot of them are quite simply true color, but taken with a sensor (CMOS, CCD) that doesn't suffer from the limitations of the human eye.
E.g. look at this image of the Horsehead Nebula:
All that color is real. It's there, in the photons reaching you. But your eye cannot see it. A CMOS, however, can. This is not "false color", although saturation was likely increased in post-processing, in addition to what the sensor can do. But the hues are probably real (e.g., the red you see in the image, or the blue, was present in the photons hitting the sensor - albeit at a lower saturation level).
(An astute observer may object that the eye and the CMOS don't see the exact same hues, but let's not go down that rathole now.)
"False color" means when the image shows green where the CMOS (or the human eye, if luminosity was higher) would see red, or something like that. This is not always the case with images of nebulae and galaxies; in fact, if the image was taken with visible light, chances are the hues are preserved.
Proper false color images are those taken in UV or IR, and then artificially converted to visible light. This is an example of it, the Sun in ultraviolet:
Now, to answer your question:
Unfortunately, even from a near distance, most of these objects won't look much better. They are, after all, faint, rarefied clouds of dust and gas. They are just not bright enough for the human eye to see color.
There are few exceptions. A notable one would be close binary systems where the components are stars of very different temperatures. Kind of like Albireo, but much closer. From a starship, looking at the two stars orbiting each other, you'd see very clearly a striking color difference - perhaps a large, somewhat dim, deep red star, and a blinding, crisp dot of bluish white light, the smaller and more active companion.
The views from the center of a globular cluster undergoing a compression phase should be pretty spectacular, too. Night would never be dark on a planet in the middle of the cluster.
Best Answer
Well, First off, you can see the Andromeda galaxy with your naked eye from a dark place on a clear night. You should try it if you can. It looks like a smudge of appreciable size, not like a point. So half way between the Milky way and Andromeda, both would look like smudges twice as wide as Andromeda does from earth. I think a standard point and shoot camera is slightly better than the naked eye, but not a whole lot. The other way to think about it is to consider the power of the lens used to take the picture. Telescopes are usually between 10 and 100 power, although more is possible. A point and shoot is usually 1-3X I think. The naked eye is 1X of course. But long exposures "see" much more than the naked eye. So to get 10X you would need to be 90% of the way to Andromeda so the remaing distance is 1/10th of the way to Andromeda, to get 33X power equivalent, you would need to be 97% of the way to Andromeda, etc. I am guessing you would see some structure at 10X, particularly with a long exposure from space, but to get the equivalent of the truly excellent pictures you see on the web or in astronomy magazines you might have to go to 33X or even 100X. For 100X you would have to go 99% of the way to Andromeda. Again, your point and shoot with a long exposure is probably three to ten times better than your naked eye.