I know I post a lot about the treks I take through woodsy suburbia with and without my dog. For one thing, I like posting the pictures and bragging about how far I went on my various excursions. Not cool, I know, but I get some satisfaction there.
Anyway, the area I live in or near is pretty special to me, but it isn't special in the sense of being singular or unique.
If you live in a neighborhood with sidewalks, you actually have a good area for walking, even if it isn't as nature-filled or dog-safe (hullo, cars!).
If not, I encourage you to visit your county parks and recs website to check out places you can walk intended for that purpose. You might be surprised. If you live near a neighboring, non-hostile county, I recommend checking their resources too. My county has no parks to speak of. No safe parks period. But the county where I was born and where I work has some serious acreage designated as recreational space, including well-maintained trails with restrooms.
Also, you might want to try Google Earth and http://www.gmap-pedometer.com/ to find less official walking trails and pathways to enjoy. Just zoom down and start looking for things that are not roads. Or for roads with sidewalks. I use Gmap to plan some of my outings, especially those going into unfamiliar territory.
You never know what you might find in terms of scenery and special places.
If you're willing to drive, try looking into your local or semi-local state parks. I'm too faraway from mine, but if I could get to one in 30 minutes or less, I would be there once a month, at least, weather-permitting.
And if at all possible, remember to take only photographs and leave only paw prints.