Jumeirah's hiking trails are not a popular pastime. It is very hot in the city, and walking is not common. Everyone travels by car or cab. So your walking routes in Jumeirah will probably be limited to the beachfront and the surrounding shopping centers.
You can also combine shopping with a beach vacation by ending your Jumeirah walking itinerary at the city's chic oasis beach, Jumeirah Beach Park. It is not only very clean and stunningly beautiful, but also everything is organized to the highest standards - after swimming you can play volleyball, go to a restaurant and even watch a play.
Continue the tourist route beyond Jumeirah - there are many more interesting things in Dubai: the tallest building on the planet Burj Khalifa, and a beautiful garden of flowers Miracle Garden, and the twin towers Emirates Towers, and the largest shopping center in the country "Dubai".