You'll want a small tree with a large canopy for shade. Fringe tree is an attractive flowering tree native to the U.S. Boxwood are coarse and dense. Placing them close to the patio will make the space feel small and intimate. On the other hand, plumbago is fine and delicate. It would make the patio feel larger and open. You can do either. Many people also choose to place their flower or butterfly gardens within view of the patio.