Definitely the 2000's. Although TV changed so much over that decade it doesn’t feel like the same era by the end of it so I would say 2000 to 2005 to be more specific.
It is the rise of HBO and premium TV, the Jossverse is at its peak, there were new platforms releasing more and more quality shows (without the sheer quantity of new shows feeling overwhelming like it does now), there was a good mix of fun and serious shows without every show wanting to be a 60 minute prestige show, and people still tended to watch shows at the same time.
It is crazy to look at the shows that either started or were still on during that 5 year period
Sopranos - from S2, Oz - last few seasons, Six Feet Under, The Wire, Carnivale, Deadwood, The West Wing, Buffy - last half, Angel, Firefly, Veronica Mars, Dead Like Me, Wonderfalls, Freeks and Geeks, Arrested Development, Curb Your Enthusiasm, Da Ali G Show, Entourage, Extras, The Thick of It, Office UK, Phoenix Nights, Peep Show, Spaced, Brass Eye, Family Guy, Its always Sunny, Band of Brothers, 24, State of Play, The Shield, Lost, House, Desperate Housewives, Rescue Me, Prison Break etc
And did Doctor Who reboot start in 2005?