|MadSci Network: Astronomy|
You are correct that sunlight keeps us from seeing stars in the daytime. This is because the atmosphere on the side of the earth facing the sun scatters the light from the sun, making the sky so bright that it drowns out the light from the stars that would otherwise be visible at that time.
So, the stars are always there, you just can't see them in the daytime because they are dimmer than the sky. The question is, which stars can you see at night, and which would you be able to see during the day if it weren't for the sun?
The important thing to remember at this point is that, while the earth rotates once per day, it also revolves around the sun once per year. The stars, at least for the purposes of this answer, remain fixed in space. Therefore, during the day, the stars which are "up" (that is, above the horizon) are mostly those which lie in the direction of the sun, those that lie due east, those that lie due west, and those in between these extremes. It gets dark when the earth turns your location away from the sun, and the stars that are visible then are mostly those that lie in a direction away from the sun, plus those that lie to the east ans west and in between.
Now, since the earth moves around the sun once per year, the stars that lie in the direction of the sun are constantly changing. Six months from today, the stars that lie in the direction of the sun will be those that today lie in the direction opposite the sun. (You can prove this to yourself using a couple of tennis balls - pretend that one is the sun and that the other is the earth. Put the "sun" on the floor in a room. Then place the "earth" to one side. Notice that, from the "earth," one wall - the "stars" lies opposite the "sun," while the opposite wall lies on the opposite side of the "sun." Now move the "earth" to the other side of the "sun," and see what happens.) So, the exact stars you can't see today will be those which grace the night sky in six months.
So, no, there are no stars that you will never see thanks to the sun. Of course, at any given location on earth, there are some stars that can never be seen because they do not rise above the horizon. For example, the latitude of Myrtle Beach, SC, is 33.68 degrees north. This means that stars with declinations (analagous to latitude for stars) of 56.32 degrees south or further south will never rise above the horizon there. However, to see these stars, you just have to go further south. And you can console yourself with the thought that those people living at temperate latitudes in the southern hemisphere cannot see a lot of the stars up here in the north.
I hope this helps answer your question.
Try the links in the MadSci Library for more information on Astronomy.