I think the neighbor might actually want to rethink this. Having kept honeybees in the area can actually reduce the number of feral bees, or other stinging insects. And because they are gentle, this might result in a decrease in stinging.
I do think that if you keep bees in an urban or semi-urban environment it's important to take steps to limit exposure to neighbors. This means pointing the hive entrance away from common pathways, putting in a fence or bush that will encourage the bees to go up (they are generally above head level after 10 feet). Making sure you provide water so they aren't at the pool next door looking for a drink. And educating the locals about bees. (Sending around jars of honey doesn't hurt).
Bees will range far and wide, sometimes as much as 3 miles to find flowers. So it almost doesn't matter where the hive is, the poor little creatures travel. Oddly, beekeeping in a suburban neighborhood might result in more honey than in a rural area, because the concentration of flowers is often higher.
Then again, if she's only getting a few quarts, she's a pretty low-key beekeeper. The hives near me average about 40 lbs a year. Oh, and I spent a summer apprenticing at the local apiary to learn before I get my beehive up and running this year. I wasn't stung once. And that's with having to actually handle the bees. I'm even at a point where I don't wear gloves unless it's honey harvest time. Bees are much gentler than I ever realized, it's that they look a lot like other things and they get a bad rep.
A tip for anyone who carries an epi-pen, carry an anti-histamine too. It will help dampen the reaction significantly. I'm allergic to spider bites (probably only one kind, but they can't test it) and I carry both. It was the anti-histamine that saved my life.
