I've visited the Little River Regional Park several times over the last month. It's actually in Orange County, about a mile north of the Durham/Orange border, and it's run jointly as a partnership between the two counties. There are two main hiking trails, mountain bike trails and an ADA-friendly loop paved with asphalt. The latter is referred to as an interpretive trail, though I didn't discover anything that needed translation.
The two main trails go down by the Little River itself which is more creek-like than river-like. The south river trail took me about 45 minutes and the ridge/north river loop took about 90 minutes. Both are relatively easy and largely unused -- in three times hiking there I've seen a total of four other people hiking. The trails are well-marked with signs with the glaring exception of one point on the south river loop; because of that J and I ended up walking around for a while on some really nice private paths that border the park which you're really not supposed to do. There are no signs on those paths either, so it took us a while to figure out which way to go to get back on the right trail. (And no way were we going to retrace our steps, though I did have moments of horror imagining getting lost in a park that close to my house.)
There are some nice clean bathrooms there (definitely a plus), a butterfly garden area (that was roped off) and one of those horrible generic plastic and metal climbing structures that any kid in his/her right mind would be bored to tears from after ten minutes. Also, there's a picnic shelter and some open spaces for tossing a Frisbee around.
I've spotted lots of animals there -- deer, turtles, groundhogs (I think) and rabbits. I kept having the feeling when I was hiking that there might be a bear just around the corner, but fortunately never saw one. It's definitely recommended if you're interested in getting lost in the woods (figuratively) for a while.