I’m a ground watcher. Some of it is due to having uneven sidewalks and potholes to avoid. But mostly, it’s because I live in my head. When I am walking somewhere, I typically have my headphones in and I’m daydreaming. Sometimes I make a concerted effort to concentrate on the world around me, especially if it’s a beautiful day, but I always end up back inside my head.
Back in the day, I used to visit my sister in her apartment in the village. Is that still a term? It’s been a long time. We used to walk all over Manhattan. My sister would point out how to tell a New Yorker from a tourist. Specifically, all tourists walked staring up at the skyscrapers and billboards. All New Yorkers kept their eyes on the sidewalk navigating the clear channels of concrete through the shoals of dog shit. It was before the no dog droppings even in the curb law. As I recall, that law also changed the smell of New York.
It depend were I am walking , if I am at a park I will keep my eyes on the ground b/c I don’t want to step in dog shit or trip over something . People are really bad about cleaning up after their dogs here. In my house I will look down to made sure I don’t step on my small dog. I have found money when looking down. 
I scan and pan same as I do on the bike. Partly in the hope of seeing things that I find interesting and partly old habits of threat assessment.
I’m checking out the local storefronts and at the same time assessing the pedestrian and other relevant traffic 20-150 yards in front of me and off to the sides, and occasionally glancing at the sunset in the sky or the seagulls perched on the telephone poles or watching the kids get into the SUV with their mom and so forth.
When I’m walking for exercise in my neighborhood, I’m looking at the ground, thanks to uneven pavement (I tripped and sprained my wrist about two months ago, so I’m even more vigilant), and I’m also looking around. I don’t keep my gaze fixed, I look up, down, around, down, up, wave at neighbors, make kissy noises at neighborhood cats, etc. etc.
Me too. I see legs too, so I know if someone is coming my way.
If I’m looking at the ground it’s usually because my brain is preoccupied with something directly, so the best place for my passive gaze is where obstacles are most likely to appear suddenly.
If my brain is not occupied, and I’m just passively listening to a podcast or music or whatever, my gaze is more likely to be active and looking around me more.
Also, instinctively I will check for traffic at crossings and corners, for other pedestrians coming towards me, and other obstacles like tree branches and cars leaving driveways.
I’m not sure what I do indoors. Probably look ahead, as the floor ought to be flat and familiar.
I’m scanning the crowd, trying to pick up my tail so I can shake them. They work in teams, you know. The tall older gent looking intently in the shop window (women’s blouses); the woman with the baby carriage (been with me for 4 blocks and 3 turns; the guy who changed caps and reversed his vest, the police officer - reflector shades - nonchalant attitude. It’s hard; ducking into shops and restaurants and bugging out the rear entrance smashing through the food servers and preparers. I’m king of the subway though - in and out of cars - sprinting up landings - sliding down escalators (though those bumps leave some painful bruises). That’s me, just an ordinary guy out for a stroll - but still they follow - now it’s drones.
I look all around and make lots of eye contact on the subway.
Leads to many memorable experiences.
Depends where I am. Generally like to maintain good situational awareness, so in urban environments I tend to divide a good portion of my attention between scanning other people and traffic. When I’m in natural environments the default setting tends to be more ‘wide angle lens’, taking the entire scene in at once with less eye movement/scanning.
I live in the desert. I look down.
Why on earth were you skiing in the parking lot? 
My head is on a swivel whether walking, driving, running, etc. I’m easily distracted!
Walking? Basically just straight ahead. And my peripheral vision is sufficient to notice stuff on the ground I need to avoid, or hotties that I can quickly glance at.