If you could shield yourself from the radiation (which would kill you in a few days), then you could get a little closer than Earth, but not much closer. On the surface of Mercury which is still 35 million miles away from the sun, the temperature is over 400 degrees, so you’d be burnt to a crisp! Pretty much all stars are the same, so there wouldn’t be much of you left to touch the star!
It isn’t possible to get very near one, as apart from the heat and the radiation, the uppermost surface of a star is a plasma that would quickly destroy anything near it.
It is a bit difficult to say where a star begins because it isn’t very dense. A good analogy is the Earth itself; you can’t touch the atmosphere easily. So it is a bit hard to say how you would ‘touch’ a star, more ‘wave your hand through it perhaps, because it isn’t very dense. (Of course, you can’t get there in the first place.)