One of the nicest dog-friendly cafes that I go to is the Canning River Cafe which is located near the river in Cannington. After you have indulged yourself on their lovely food and drinks, you can meander the walkways they have in the park next door, and over the bridge for more walking, which will please your pooch no end.. There is plenty of parking, but I would recommend you book a table if you are going for lunch as I have seen the place fill up very quickly even during the week.
If you just wanted to take your own food, there are excellent facilities there including BBQs, so make a day of it with the family and of course, the dog.
I will often spend another two hours there after lunch as there is so much flora to see, and many birds visit the area. There are lots of benches to just sit, breathe, relax, and drink in the peace and tranquillity of the area. Aaahhhh, doesn't get better than that!