A few years ago the Hipparcos sattelite measured distances to ~120,000 nearby stars, so somewhere there is an exact answer to this question. I don't know to what magniture Hipparcos could measure parallaxes for, and whether it could see the dimmest M dwarfs 100 light years away, so it may or may not have observed all the stars within 100 light years. Given how dim M dwarfs are, I would guess it probably didn't. In other words, somewone probably figured out exactly how many stars in the Hipparcos catalog are withi 100 lightyears, but I don't know that answer, or whether that ould be all of the actual stars within 100 lightyears (~30 parsecs). So, here's an estimate. In our part of the Galaxy, the average distance between stars is about 1 parsec. (30 PC~100 ly). 4pi/3* (30 PC)^3 is about 113,000 stars out to a distance of 30 PC or about 100 lightyears. Now, about half of the star systems are binaries or multiple systems, so 113000 + 113000/2 is about 170,000 stars. That's a lot! As for how many have planets, well, we have detected several hundred extrasolar planets, but they are almost all very large planets orbiting very close to their parent star, simply because this is what is easiest to detect. The more we look, the more we'll probably find, so there are probably many thousands of planets within 100 ly of our solar system.
Thanks, missed that. The 170K number is a bit disingenuous as it counts binaries as two systems. And if you want to pretend to count M dwarfs...