Coconut palms can grow in a small space. They're tall and thin. 20 ft by 20 ft is plenty, so the 7 palms discussed above could fit in 2800 sq ft, or about the size of a suburban home. They can also grow in nothing but salt water and sand, land unsuitable for just about anything else.
source: I grew up on a tropical beach with coconuts all around. See my username.