The first Heroic I finished was Shadowfang Keep. I can also do Blackrock Caverns (skipping the 2nd boss), Halls of Origination (skipping the 'portal' boss), and all of Vortex Pinnacle. I just recently beat the first boss in Grim Batol, and can do the first 2 bosses in Deadmines.

I think after patch 4.2 and the current Valor gear becomes purchasable with Justice Points, things will get incredibly easier. My team's average item level is about 345.