Pondless Backyard Fountain Pond and Waterfall. Even without the fountain, which in Az will grow algae like nobody's business, I think the idea of softening up the patio with a little rock garden with plants mixed in.
Idea for the side of the house? A Thai rock garden, or rockery, is an excellent way to decorate an uneven or unattractive part of the garden and can be employed well in both large and small spaces. - The Thai Landscaping Experts
Where the dogs have worn the path down. Utilize reclaimed pallet wood to build a rustic wooden walkway. You can use it to link two areas of your backyard, or to add some character to a quiet corner. Get the tutorial at Funky Junk Interiors.