I'll be alone in NYC in June and plan to go to the Columbus Circle flea market on Sunday. Any suggestions on where to have breakfast where I won't stick out like a sore thumb in the brunch crowds?

Do you mean Columbus AVENUE flea market? (that's around 76th and Columbus avenue--Columbus Circle is at 59th street and Broadway, about a mile away)
Some "brunch" places do open early enough for a real breakfast, plus there are a couple of plain old diners/coffee shops . What time and price range are you thinking of, and what's the worry about "sticking out like a sore thumb"? At the trendier brunch places, the worst you'll have to deal with is a long wait for a table...

There are a few places that serve brunch and then there are several coffee places. Columbus Ave is well endowed with eateries
You won't stick out like a sore thumb, many people wander out in the am, grab their paper and go have brunch on their own..eating single in NYC is nothing anyone pays attention to.

I have SUCH a taste for some chicken satay and coconut rice from Penang, on Columbus, not that far from the flea mkt..go there, have some for me

Nothing to do with breakfast, but may I recommend that you check out the Green Flea, IS 144, which is on Columbus Avenue and 77th -- right across from the Museum of National History. I think that's the one you mean, although there is a Columbus Circle small market open daily. Of course, you really should check out 26th Street -- lots of markets here, including the Garage, the Annex, etc. Avenue of the Americas. Go to www.collectors.org for a complete run-down of markets, addresses and hours if you're into flea markets.

B/

Or...just bag brunch altogether and load up on the cider donuts at the entrance near the plants!

Actually, if you go over to Amsterdam Avenue from 79th up to 86th, the street is lined with places to have brunch. The most popular ones get very crowded, so there may be a wait -- like E.J.s at 82nd, Good Enough to Eat at 84th, and one of my favorites, the Popover Cafe at 87th St. Just wander the street and see what catches your eye.

Those are all within striking distance of the Columbus Ave. flea market (bet. 76th and 77th) And don't worry, no one gives a second glance at those dining alone -- I've done that plenty of times, me and the NY Times.