Single -speed cruiser? I'm guessing a coaster brake and a narrow OLD.

The Shimano SG-3C41 is nice. It's used on probably 98% of the OEM three speeds in the USA. Shimano only offers a twist shifter for it.

The Sturmey Archer SRC3 has a beautiful polished aluminum shell. S-A offers a twist, trigger, dual paddle, thumb and bar end shifter for it. S-A is the only IGH manufacturer to offer extensive aftermarket support of their hubs in N.A.

The SRAM iMotion3 is a new design that shifts fast both up and down and has its shift cable inside the drop outs. It's only available in 130mm OLD, and SRAM only offers a twist shifter. The coaster brake is roller actuated.

Note when you compare prices that Sturmey IGHs typically come complete with all fittings and a shifter, and Shimano and SRAM IGHs usually require you to buy the shifter separately.

HTH,
tcs