My best experiences playing and GMing are definitely at levels 5 & 6. I picked 5th, but it varies by class - for Wizards 5th is awesome, for Sorcerers & Fighters, not so good. Of course it's also good to work up to these levels if possible in a tabletop game (PBEMs may be better off starting at 5th, esp in a one-shot), at least from 3rd, preferably from 1st. IME the game gets less fun after 8th, which oddly was not my experience of 1e! Although 3e is much more focussed on "supporting" high level play, in practice that usually means "bigger dungeons with bigger numbers", which for me is a pain to GM and yet doesn't offer a significantly different play experience than 1st-3rd. Basic/Expert/Companion/Masters/Immortals I reckon had the right idea - different types of play at different levels is the way to keep the game fresh & exciiting.
what should be done is to revise the XP tables & default demographics to facilitate play at this level. Eberron seems to have worked on the NPC demographics (no Wiz-20s under every bush), and there are a reasonable number of CR 5-8 monsters, but the standard 3e XP table is still there and still causing trouble for GMs & groups who prefer mid-level gaming in a mid-level world.