Hey there, we are starting our first beehive this spring, buying the hive and bees commercially. We were going to put the hive in a corner of a fenced yard about 10-15 from the garden.
My question: if I won't be directly in front of the hive, is 10-15 feet away while gardening a safe distance to not "aggravate" the hive and get stung purposefully? I have little kids playing in the garden too.
I let a pollination service use my land for hive locations. Ten feet has been a safe distance for me from the honey bees. In late autumn the hives attract Yellow Jackets that try to raid the hives, they are very aggressive.
ten feet is pretty reasonable. fifteen feet would be just fine. there are also a few easy strategies that would allow you to work even closer to the hive without disturbing the bees.
raise the hive up off the ground a bit. the bees will typically take an upward trajectory when they're leaving to forage. if they're already higher up, they'll be well over your head before they reach your garden. keeping a hive up off the ground also helps avoid ground-level moisture, rodents, predators, and probably some other pests. in my region, I consider 18 inches a minimum, and usually shoot for at least two feet. higher is just fine so long as the hive is stable and can be managed safely.
aim the entrance away from your garden. the bees won't only forage in the direction the entrance faces, but they do tend to fly that way for a while before heading wherever they're off to. East or South are usually considered the best orientations for the entrance in the Northern hemisphere, so if you can manage one of those (or somewhere in between) while facing away from the garden and not into a fence, you'll be in good shape.
plant a little hedge or screen between the hive and your garden. it will direct the bees upward as they leave. make sure to leave them some room, though: you don't want it too close to the entrance.
one possible caution: if you're going with conventional Langstroth equipment and management, your bees might very well be rather grumpy. frame hives generally require a fair amount of manipulation to keep them functioning the way they're designed to, and that manipulation doesn't always go over well with the bees.
and one other note: they aren't likely to spend much time in your garden. they've got thousands of acres to choose from, and the proximity of the hive is where they do most of their, um, defecation. I don't know if that's why they don't forage in the hive's immediate proximity, but it would make sense. decent fertilizer, though, if rather slow to accumulate.