the sun - What's the mass of the interstellar neighborhood of the Sun?

Very roughly: $3.5 times 10^{33}kg$, or 1800 solar masses.

Here's how I came by that number, it is a very rough approximation.

The major mass components of the galaxy are stars, the interstellar medium, and dark matter.

According to the HYG Database there are approximately 1000 stars within 50 light years of the Earth. The average mass of a star is 0.2 solar masses (thanks to Rob Jeffries in the comments), where a solar mass is about $M_odot approx 2 times 10^{30} kg$. This gives us $4times 10^{32} kg$ of stars nearby.

The interstellar medium (ISM) is primarily atomic hydrogen, and has an average density of 1 proton per cubic centimetre, although it can vary widely in different parts of the galaxy. A proton weighs $1.6 times 10^{-27} kg$, so a 50 light year sphere of "average" ISM will weigh about $7 times 10^{32}kg$. We can do a little bit better than that though. Our solar system lives in the local fluff which is a cloud in the local bubble. The local fluff has a radius of about 15 ly, and a density of 0.3 atoms per cubic centimetre. The local bubble is about 150 ly across, and has a density of only 0.05 atoms per cubic centimetre. Using these figures instead we get an approximate ISM mass of $4 times 10^{31} kg$.

This is an order of magnitude smaller than the contribution of stars, and our estimate for the stars could easily be off by more than 10%, so let's err on the high side and say the total mass of stars + ISM is $5 times 10^{32}kg$.

We don't know how much dark matter exactly is in the galaxy, but if its similar to the cosmological average then there is roughly six times as much dark matter as baryonic. If this holds true locally, then there is about $3times 10^{33}kg$ of dark matter nearby.

So, a rough estimate says there is about $3.5 times 10^{33}kg$ of mass within 50 light years of us. This is equivalent to 1800 solar masses, or $2 times 10^{60}$ protons!