It should be limited to stars only and only stars that are the "most significant" massive object in their area.
To determine whether a star is the "most significant object" is fairly simple.
1) Out of the more massive stars in the system than the one you're testing, determine which one has the largest gravitational pull on the "test" star (this is a very simple calculation).
2) Find out the point between these two stars where their gravitational influence is equal (this again is simple, it's called "sphere of influence" in Kerbal Space Program btw).
3) If this radius is greater than a magic constant the devs make up, then you can jump directly to the star, otherwise you can't.
The idea is that you should be able to jump directly to Proxima Centauri, but not to a red dwarf closely orbiting a much larger star.
Also, upon jumping into the system, you should be able to choose the star you jump to if there are more than one valid candidates.
As currently the fuel usage is quadratic (or close to cubic in the case of larger drives) the fuel usage of these jumps would be insignificant. I don't think that's well balanced, so I suggest a minimum fuel usage be introduced, I suggest 0.1% of the ships mass. This is the amount of fuel required simply to open the hyperspace tunnel, even before extending it.
This allows for about 30-40 minimum jumps for most ships I looked at based on their mass and stock fuel tanks, so hardly a significant burden but a small cost on doing lots of micro-jumps. Of course it could be lowered to even 0.05% if people think that's burdensome.