I'm not an astrophysicist, but a chemist, so this comes from a less than ideal background.
The key features of a neutron star for nearby objects are the disproportionately large gravitational effect they have for an object of their size, and the tight beams of intense radiation they emit from their magnetic poles (not necessarily their rotational poles, look into pulsars).
A neutron star could be an object abut 10 km wide with the gravitational effect of an object double the mass of our sun. A star system with a habitable planet similar to ours is more likely to orbit the neutron star than it is to orbit that planet's star. They form from supernova, which would have obliterated nearby star systems, so it would most likely be an object that orbited in from far away before capturing the planet and star. This would likely make the neutron star a very distant object in human terms. Another possibility is that the neutron star swept up an accretion disk while passing through stellar dust clouds and built the star system around itself. Jupiter is almost massive enough to have become a star, so something not much bigger could provide the 'sun' of this system, but be an interesting case where a habitable planet does not orbit its own sun. This odd configuration might cause a regular cycle of ice ages and global warming much like ordinary winters and summers as 'Jupiter' moved relatively closer or farther over the course of decades.
I think the high energy 'lasers' emitted by the magnetic poles would sweep out two cones of space (hopefully outside the orbital path of the planets) which would be utter kill-zones for anything we understand as biology or technology. One could theoretically navigate around the beams, but their precession around the neutron star as it rotates is so fast that the window of entry into those cones of space would only be a few seconds at best. I'm unsure a vessel even could pass through the kill-zone fast enough at sub-light speed.