Not sure if you are talking about the fun run or a hike with Pets. I can offer some suggestions for hiking with pets for sure.... close to town.... not to difficult.... etc.
As far as a fun run (pets can go too) maybe the 15th (Friday). After a good week of wheeling, maybe just head out to Davis Canyon (no low 4 wheel drive needed) for some fast sand runs... some sand trap golf... some hiking... lunch... This will take us past Newspaper Rock too.