I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, see Nick Proudfoot's thesis). These are very nice symplectic manifolds (hyperkahler and exact, in particular), so I feel like their Fukaya categories should themselves be nice, but I've never found a good reference on them.
The marquee example of this is Nakajima quiver varieties. I would be very interested to hear anything about the Fukaya categories of these.
A question of particular interest to me the Floer homology of images of invariant Lagrangian subspaces in the quotient.