Experts and BHG readers answer.
Quick growing tree for shade
Keep in mind that the faster that a tree grows, the weaker its wood and the more likely that it will suffer broken limbs in storms. It's best to choose a tree with a moderate growth rate, and that will last a long time. Even trees with supposedly slow growth rates can put on several feet of growth per year if they have good soil to grow in.
Choosing the best tree for your location depends on what soil type you have, how much space is available, and your hardiness zone. You can search for trees that fit the criteria you choose in our plant encyclopedia advanced search function at http://www.bhg.com/gardening/plant-dictionary/advanced-search/