Your question is a little confused. The "stars" are not the object of space exploration as it relates to space shuttles and manned flights and surface probes. The solar system--and only the nearest portion of that--is the object of these sort of space exploration.
The "stars," including our "star" (better known as our Sun), are the object of a different kind of space exploration. This kind of exploration centers around various satellites that perform various imaging and collection missions and that operate in space in one of two or three select modes. These are a couple of examples out of scores of possible examples.
To explore the Sun, we employ satellites like SOHO, which orbits Earth's First Lagrangian Point (L1), which suspends it caught between the Earth's and Sun's gravitational forces. It has a continual view of the Sun, which it takes images of through various ionizations, and collects data on solar wind, the Sun's corona and all plasma and gaseous layers all the way down to the Sun's deep core.
To explore the cosmos, Hubble takes images to surprising depths far out into the universe, lately finding the farthest known galaxy, which is called galaxy MACS0647-JD. SPITZER, NASA's first infrared telescope satellite, helped Hubble narrow the field to find MACS0647-JD.
Other satellites engage in cosmos mapping, like the mapping of the locations of dark matter, and triangulating cosmic occurrences, like impending X-Class solar flares, and identifying component characteristic of the cosmic microwave background.
The value of this sort of space exploration is (1) practical and (2) pure knowledge. First, it is valuable for practical reasons because, for example, Earth's magnetic shell--the magnetosphere--incurring holes from solar wind particles will be poor protection from a direct-hit M- or X-Class solar flare, and we need to know how to protect our communications and other satellites. Second, it is valuable for pure knowledge because humans can't seem to stop asking questions that only pure knowledge can answer: What holds universe together (what is dark matter?)? What forces tipped the cosmic scale in favor of baryonic matter (us)? Where is the interface between quantum physics and Newtonian physics?
So, if you mean the first kind of space exploration, I'm not so interested in that, personally, and can see budget cuts there not doing a great deal of harm as I can't see the practical use of exploring Mars for the remnants of ancient waterways. If, however, you mean the second kind, I am rather more interested in that and sigh sadly whenever I hear of budget cuts in these areas. I find the results of this space exploration of rather more practical value.