I have a headphone amp that runs 6v6 tubes. My favorite NOS tubes are listed below.
STC/Brimar 6v6g (1930s era). well balanced sound, no single area of emphasis. Hard to find and somewhat pricy. My current favorite.
Westinghouse 6v6g: (1940s era) similar to the STC, but a little more bass emphasis. More easily found than the STC and less expensive. Goes well with brighter input tubes like Brimar 12au7s.
Mazda 6v6gt: (1950s era) this might be the tube you’re looking for. Airy, great soundstage, a little more emphasis in the high frequencies, but not too much. I pair them with warmer/darker sounding input tubes like Mullards to balance them out. Somewhat easy to find and not crazy money.
Sylvania 6v6gt: does no harm, but not a standout in any area. Cheap and very easy to find. A good tube to choose if you just want to “try it out”.