Not Caymanian. And not dead.
Chief Standing Bear and Justice Earl Warren would be fine choices.
Politically?
I wouldn’t change the $100 bill. Supposed to be Benjamin Franklin but looks more like Jack Benny to me.
A bad idea. Sure he was a good inventor and painter. But are you familiar with his political ideas?
Alfred E Newman
Just to make a change, I’d move away from portraits of people. I’m British; would like to show, on the reverse side of different denominations of banknotes (keeping the monarch’s portrait on the front side) – pictures of various British technical / architectural inventions / achievements of note. I’m a fan of railways and steam locomotives, so would like one denomination to show a British steam loco of some “date, shape or make”.
Me too. I think it’s a great choice.
I also believe it’s one of the few times a living person (besides the reigning monarch) has appeared on the currency of a western nation while they are still alive, too.
As for me, I’d like to see Captain James Cook, Abel Tasman, John Simpson Kirkpatrick and Sir Charles Kingsford-Smith on Australian banknotes, FWIW.
(maplekiwi wrote: “Love the idea of Jane Austen on the notes.”)
Not me. I hate the bloody woman – find her novels completely unreadable (and I’ve tried, and tried, with them). When the JA £10 note comes out, I’ll want to boycott it: change any that I get, for fivers, as quickly as possible.
Jim Henson was what first popped into my head! 
So I guess my collection would be childhood luminaries: Jim Henson, Walt Disney, Mr. Rogers, Dr. Seuss, Mr. Wizard, etc.
The reverse could feature what they were best known for (i.e. Mr. Wizard with a child performing an experiment) with a short blurb about their life, perhaps.
Well, Canada’s stuck with the monarch on the coins. But she’s also inexplicably on the $20, and there should immediately be replaced with Frederick Banting.
The other ones are fine.
If I was redesigning American currency:
$1: Washington
$2: Jefferson (meh, why not)
$5: Lincoln
$10: Martin Luther King Jr.
$20: Norman Borlaug
$50: Grant’s underrated, keep him
$100: Armstrong
I don’t really see the need for any faces on currency. I like the comment upthread about something useful, like a conversion chart or something, but I would be fine with the front being a variation of the back. Just a big font with the amount.
No need to idolize anyone, IMO. Just let currency be functional.
Seven, you say?
Well, that’s easy, then:
Destiny, Death, Destruction, Dream, Desire, Despair, and Delirium
we could start calling them Ddollar bills or Endless money. 
–G!
There’s no such thing as a one-sided coin.
Wayne Gretzky on the $100
Neil Young on the 50
Les Stroud on 20
Robert Bateman on the $10
Bubbles from TPB on the $5
Rich “Uncle” Pennybags on all bills, in various poses.
$1 - Joey Bada$$
2 - Travi Scott
$5 - A$AP Rocky
$10 - Too $hort
$20 - Ke$ha
$50 - Ma$e
$100 - Curren$y