Is the danger presented by micro-meteorites equal everywhere in space, or does space around a planet see increased danger, because its gravity increases their concentration?

For the same reason there’s a rough plane of ecliptic for planets in the solar system rather than a randomly-arranged sphere, meteors are going to be concentrated at certain orbits and in certain directions, as those which deviate too far from trajectories which place them in stable orbits, send them into the atmosphere or slingshot them out into space.

For the same reason, you’ll see most of the orbiting meteors travelling in the same direction, since those which oppose that direction are more likely to have massive collisions which send them flying out of orbit or into the atmosphere. In the short term there’s always going to be a fair bit of chaos, but over time Brownian motion of individual meteors will create a rough equilibrium.

This means, while you’re probably more likely to see impacts inside of a gravity well, they will be by objects travelling at roughly similar speeds in roughly the same direction, and thus much less damaging than the more rare but utterly catastrophic random impacts you’re going to see in interplanetary space with objects the speed of which becomes additive to the force of the impact. Something the size of a pea hitting you at a net velocity of a few kilometres a second in orbit may be damaging, but survivable. Getting hit with something the size of a pea travelling at a net velocity of a few thousand kilometres a second in interplanetary space will leave nothing but an expanding cloud of dust and plasma.

The risk would be about the same, I think. The planet may not concentrate the danger because the planet’s gravity sucks the meteors into the planet thus vacuuming them away.

Fortunately, most are small enough that they burn up in the atmosphere long before they strike the earth.

Following from what @SmashTheState wrote, one might likely reduce the risk of collision by traveling outside the plane of the ecliptic… though that might require more fuel and the risk might be deemed so small that reducing it that way might not be thought worth the effort.

In the Solar System, space contains on average five atoms per 1cm3. Interstellar space, between stars, contains around one atom per 1cm3, while intergalactic space, between galaxies, contains 100 times less. I would guess the concentration of micrometeorites would fall off at least as rapidly. However, Inter galactic ships would have to move at near light speed to get anywhere and collision with even a speck of dust would be catastrophic.