Things to consider: Is this area in full sun? Do you want high-maintenance or low-maintenance plants? Do you spend time out there in the winter? Do you want it to look good year-round?

Of course bananas, brugmansias, cannas, elephant ears, gingers are quintessential for adding a tropical flavor, but die back with a hard frost and so dried leaves, stalks will need to be removed annually, but if you're up for that then go for it. Consider incorporating some glossy, broad-leaved evergreen shrubs, small trees, vines or ground covers for good year-round interest. I'd probably stay away from using prickly-leafed hollies or yuccas/agaves near a pool. Windmill palms are good because they don't get so huge as palmettos and pindos. Maybe you could work some Sabal minors in as they stay small -- but you may have lots of small seedlings to contend with. Are Sagos hardy in your area? Indian Hawthorn and Pittosporum are good understory, low-maintenance shrubs. Crinums are nice and have fragrant blooms. You could espallier a loquat along the fence or keep it pruned more upright. Just some ideas

Not sure if they're hardy in your zone, but (sorry for mispellings) here are some I use for a tropical look, or simply lush effect:

Phillodendron selloum
Fatsia japonica
Eriobotrya
Albizzia julibrissen
Tasmanian tree fern (genus?)
Cannas and callas
Soft-tipped Yucca's
Firmiana simplex
Colocasia
Aspidistra elatior
Acanthus mollis
Irises
Agapanthus
Hostas
Hydrangea
Magnolia macrophylla
Toona (Cedrela) sinensis

I'll think of others.

Besides palms, there are few plants that will give a more immediate tropical "oomph" than elephant ears and bananas. Try Musa basjoo, Colocasia esculenta and any number of other elephant ears (Alocasia, Colocasia, & Xanthosoma).

The larger cannas--'Musifolia' and 'Red Stripe' are among my favorites--are also easy, tropical-looking and very fast-growing plants. Hedychium species and cultivars ("ginger lilies") will provide bright flowers in addition to tropical-looking foliage. All of these should be hardy in zone 8, but will behave as perennials and die to the ground in the winter.