You'd be surprised some of the tropical plants we can grow here, but my garden is enveloping my patio on the north side of my house, and when we have cold winter weather the soil stays frozen there for weeks. This does not bode well for semi hardy plants like Bananas. Guess I'll have to start another "Tropical" garden in front of my house!
When I started planning my garden I decided to find a tree that would make a nice open canopy that had large leaves and could reach out over the patio. I went with Rhus typhina or Sumac.
Another feature I like about this Sumac is the flowers and seeds. The flowers are tight spires about 8 inches tall with tiny light green and pale pink flowers packed together, attracting lots of bees. In late summer they become bright red, and hold on the tree through winter.

I planted this tree about 3 and a half years ago and it is now about 15 feet tall and 15 to 20 feet wide, providing the perfect canopy over my tropical garden. Sure it suckers all over the place, but they're easy to pull out and I like my tropical garden to be wild and unruly!