If the given definition be adhered to, an RV-[[7|9]] would come closest for me. “with the times” but not expensive, fashionable but not posh.
Then again, “hipster” seems to also stand for a clothing style cut low or even very low on the hips (example), showing more nudity than some consider acceptable. In that interpretation, the Breezy would be a worthy candidate; and that is not a taildragger.
I do have some difficulty, though, to apply either classification to your laundry basket. Another UK subtlitity, perhaps? 
Their vehicle of choice is a fixie steel frame vintage bike with a narrow flat bar and one brake for the front wheel – fixed gear precluding the need for a rear brake. There is probably some equivalence to a tailwheel and a fixie, although arguably a tail skid is a closer equivalence? Stripped down for ‘authenticity’, that somewhat overused term borrowed from existentialism, but also nimble for urban cycling. Vintage suggests pre 1950’s. The steel frame being recycled from a shed dweller, implies a homebuilt or barn find.
My vote is for a barn find Cassutt Formula 1 racer.
When I lived in the UK, I remember there was a Cassutt for sale. I seriously considered it for a little while. Not to air race with, but as a traveller – it delivers really good speed on an O-200 engine. But soon realized it would have been one of the least comfortable traveling machines ever… 
My vote is for an O-290 powered Pitts S-1 pulled out of a hangar and bought for $10K, made airworthy at minimum cost and more ‘authentic’ by stripping the wheel pants, spinner, canopy etc… thereby despite their intention making it less like the planes most people flew in the 60s and 70s. That’s the ‘hipster’ model from motorcycling…
I’d say a Luscombe 8, retro efficient and relatively cheap.
Silvaire’s definition comes closest so far. Except it would perhaps have to be electric, powered by batteries scavenged from decomissioned Teslas.
The Stinson Gullwings would be another good hipsterplane. The Ryan PT22 would fit, too.
