Thank you all for the rec's - I wanted to shop my closet first so I've come up with a couple of options. White seems to be the easiest choice as I own a few tops in white that could work.
I would wear this in a casual "every day" sort of way, using the linen blazer for cold AC and sun protection. I'd probably pair it with white crops, white shorts, light wash crop jeans and maybe tan twill shorts.
Jaileen - I don't really own any dresses that I could wear with the blazer (I don't really wear dresses).
DonnaF- a cami wouldn't really help as I want something that works well on it's own when I take the jacket off
Joy- I've never tried cutting the sleeves off of a tee, but maybe I'll give it a try!
Sterling - I don't have any sleeveless button downs at the moment but I may add one in white. I used to have a couple of those jjill tanks too but they feel a bit too thick and fitted for me in the high heat.
Jenni - thank you for sharing some ideas!
Style Fan - thanks, I'm thinking along the same line
Angie - I'll take a look at those tanks, I hadn't seen them
cjh- answered above, and I do have a graphic tee than might work
Emily- thanks - those look like great tees!