There are a number of plants that have a tropical look even though they are not tropical, such as Eucomis, Acanthus, Cordyline, Choisya. You should be able to find some palms that will grow in your area, so if you start there, you can fill in underneath with complementary foliage plants.

Sara

Davis is the same zone as Fresno z9b here so for palms, Mexican fan palm( but they get very big and tall and makes a huge mess) fox tail palm, queen palm(both not as tall, still messy though), just a few common ones around here that I always see around, but i'm sure there are more types just do a quick search in the search bar for cold hardy palms. But then again all palms make messy mess when they start fruiting. Bananas, if your not looking for edible type and just foliage then many of the ornamental type such as musa velutina, basjoo, sikkiemeniss are very cold hardy. Refer to this link of some more cold hardy variety
http://www.musabananatree.com/

And for edible type refer to the link in the blue at the bottom.

Most bamboo is cold hardy especially those from China and Japan since it snows there.

Bird of Paradise- I don't know much about them but on the net it says they are cold hardy to zone 8, so i'm guessing your good with some thick layers of mulch to protect the main stem in winter frost.

Here is a link that might be useful: cold hardy edible bananas

Stick with the plants that are hardier to give the look without the fuss. For palms I'd recommend choices such as Trachycarpus fortunei , Brahea armata or B. edulis, Butia capitata., Brahea 'Clara', Chamaerops humilis argentea. For the bananas or Strelitzia look, I'd suggest Musella lasiocarpus,Fatsia japonica, Tetrapanax papyriferus. Small evergreen trees might include things like Eriobotrya deflexa, Nerium oleander trained as a single trunk, or the briefly deciduous xChitalpa tashkentensis 'Pink Dawn', Rhus lancea, Arbutus unedo, Feijoa sellowiana. You might also look at the UC Davis Arboretum's top 100 Plant Picks for easy to grow suggestions that look good year round without a lot of water.
I'd stay away from larger growing palms or more tender ones, no Giant Strelitzia, lose the other bananas unless you're willing to water a lot. Other tropical look plants might include things like Asparagus 'Meyers', Acanthus , Aucuba japonica variegata, Watsonias, Phormium 'Cream Delight', etc.