What is the distance between the solar systems towards the center of galaxy? The distance from our Solar System to the nearest is roughly 260,000 AU. I am wondering what is the minimum distance between two Solar Systems. Since the center of our galaxy is supposed to be more dense than the spiral on which our Solar System is situated, I am guessing that the distances between adjacent Solar Systems would be smaller. Please give quantitative figures and references to peer-reviewed journals if possible.
We don't really know what the statistics are for the frequency of solar systems is as a function of stellar density and many such systems in dense regions may be disrupted by close encounters with another star.

What I surmise you want is an estimate of the density of stars as a function of Galactocentric radius.

In the solar neighbourhood, there are 378 known stars within a distance of 10pc of the Sun, according to the RECONS project. This gives a stellar density $n = 0.09$ per cubic parsec, which includes stars of all masses and white dwarfs. However, this includes multiple systems. If we ask what the density of stellar systems is, then it more like $n = 0.075$ per cubic parsec.

The average distance between stars is tricky to calculate because of the issue of multiple systems. About half of stars are in multiple systems, with a companion at distances of anything from a fraction of an AU to $10^5$ AU, though the distribution peaks at around 1000 AU.

The average distance between systems is about $n^{-1/3}$, which is about 2.36 pc (or 7 light years).

The density of stars increases dramatically towards the Galactic bulge and then again towards the centre. However, since we would not actually detect all the very low mass stars that we can see in the solar neighbourhood, to some extent stellar density estimates rely on an assumption that the mass distribution of stars is similar throughout. There are huge uncertainties here; a lot of detail is discussed in the review by Genzel et al. (2010).
The consensus seems to be that there are of order a million stars in the central parsec, giving an average separation of 0.01 pc, or 2500 AU.

This density falls by several orders of magnitude in the first 10pc. The bulge of the Galaxy has a radius of about 2 kpc and a mass, mostly in stars, of about $2\times 10^{10} M_{\odot}$. If the average star has a mass of $\sim 0.3 M_{\odot}$ (as in the solar vicinity), then the stellar density in the bulge is about 2 per cubic parsec, with an average stellar separation of 0.8 pc (or 3 light years).