Legal Question in Constitutional Law in Virginia

Unless there's more to the story, it's legal for them to take your picture. But unless the neighborhood is private property (some are), you have every right to walk along the streets or sidewalks. The neighbors have no legal right to make you stop.

Of course, my answer assumes that you're just taking normal walks. If, say, you're walking at 2:00 a.m. and making noise, then you could be in trouble. But that would be because of the noise and not because of the walks. And the fault would be yours rather than your employer's, unless the employer put you up to it.

Even though the neighbors likely wouldn't have grounds to sue you or the company you work for, they can threaten to stop doing business there if you continue to visit. That sounds awfully small-minded to me, but it would be legal. Your employer could ask you to change your routine if that happens. And unless you have a contract that says otherwise, they might even be allowed to fire you if you refuse.