Pickles and I have several dog walking routes. The most common route takes me down Praley Street (in this case down = north), across the rail road tracks and on to a long narrow stretch of grass between the tracks and a steep wooded bank leading up to Massel street. The last time I walked there I realized this narrow stretch of grass is the closest thing Valdese has to a park anywhere near walking distance to the downtown area.
There is a park just east of town off Route 70, and McGalliard Falls to the northwest. McGalliard Falls is a pretty little place, and very well used on a warm summer day, but neither of these parks are in walking distance, and neither would be safe to walk to in any case. There is also a nice path down by the waterworks, and it does have a picnic table. People use it for walking & jogging, and lots of dogs get walked there, but it's several miles outside of town. There's the elementary school, located strategically behind Butch's BBQ & the car wash, and I see people walking and jogging around the track that circles a football field, and people can certainly use it for recreation from time to time. It's certainly within walking distance of downtown, but it isn't a park. I'd feel conspicuous spreading out a blanket and digging into a picnic basket in the midst of 5th grade PE activities.
Maybe there are other places close to downtown. Back in my teenage years I'd have been all over this place & known about all sorts of out of the way areas. But these days I tend to be a tad more reclusive, so it's very possible there are places I don't know about.
Recently there was a vacant lot of land, nice big trees etc down on Main Street. It wouldn't have been much of a park, but put up some places to sit and a few things for the kids & you'd have a nice shady RE-spite on a hot summer day. But a rich person owned it and got the towns permission to turn it into a monument to himself. I have to admit it does turn heads as you're driving by, especially if you've never seen it before. You have all these normal buildings then all of a sudden there's a dug out area with statues, stadium seating (sort of) and a fancy gate keeping people out. It'll probably be open to the public occasionally for this or that, but for the most part it's an unusable space.
Just barely within walking distance of downtown there is a good large open area - looks like it was a football field for the old high school. This was purchased some years ago (before I moved here) by this same rich person who, guess what, built a monument to himself. It's actually quite elaborate and I know cost a lot of bucks. It's called the "Trail of Faith", and it documents the history of the northern Italian Waldensians, and it is interesting and educational. I took a tour once. They have fireworks there July 4th, and it's opened maybe a couple of other times during the year for a weekend or so. And that's it. It's privately owned, and though its in easy view from Church Street, it is essentially closed to the public 50 weeks plus out of the year. Perhaps it's open for scheduled tour groups, I'm not sure, but it isn't a place you can go visit on the spur of a moment or take a dog and let it run loose. Some may argue it's not in walking distance of downtown anyhow (others may argue a whole lot more than that), but if you cut a corner or two, perhaps walk thru someone's yard, it is. If you have the physical ability to take advantage of a park, you could walk to this place.
Valdese is not a big place, so there's probably nothing to be done about it. And even if there was, I'm pretty sure nothing would get done about it. Morganton, just to the west, is quite a bit bigger and does have a nice park system, complete with river walks and such. There are parks in the area, but it would be nice if there was something within walking distance, close to downtown.