Best electrolytic capacitor

I agree, Elna Silmic II. For the big caps, Jensen 4-pole if you can get them. Otherwise, Mundorf is fine. 

Are you recapping a vintage piece of gear? If the caps are 30-40 yrs old, they most likely need to be changed out with new caps. 
Never buy NOS electrolytics. 

I’d just check images of gut shots of high end tube components that you like and see what’s in them. You’ll likely find Nichicon, Elna Silmic, Panasonic, etc. 

I find that using a bypass film cap 1/100 the value of the electrolytic soldered to the + & - tabs or wires smooths out the high end of certain components too, but that’s not anything new. 

Thank you all.

Elna Silmic II Are not available for high voltage tube power supplies.  Too bad. 

From the AN website:
"The Audio Note (UK) KAISEI range has been developed over the past years in collaboration with the engineering team at Rubycon (of Black Gate fame). Whilst working on our top of the line Black Gate replacements (which we should releasing toward end of the second half of 2016) we realised that it would be possible to put together a range of more affordable electrolytic capacitors that use all of the same materials as these supreme components (the same special electrolyte, foil and construction quality) apart from the hyper expensive and extremely difficult to produce Graphite impregnated paper, so the only difference between the KAISEI capacitors and the forthcoming Black Gate replacements is that the paper is not graphite impregnated in the KAISEI, otherwise they are the same."
I tried them in high capacitance values as coupling caps, bypassed by ClarityCap MR film caps, in Pass ACA 1.2 kit Class A monoblocks.  They sound fine after a long break-in cycle.