If I play Astral Heron directly to my battlefield, does his effect activate now, and can I play my next card for less?

Yes — if Astral Heron is the first card you play that turn and you play him straight to a battlefield you control, he sees his own play, triggers, and your next card this turn costs [2][A][A] less.

Ordering matters: the discount applies to the next card played after the trigger resolves, so you have to let the trigger resolve before playing that second card. If you play Heron to your Base instead, the "if I'm at a battlefield" clause fails at the moment the trigger condition is checked and nothing fires — and he doesn't retroactively gain it if you move him later.

Also keep the errata'd "this turn" in mind: the discount expires at end of turn if unused (CR 420.4.a).