It sort of depends what you mean by "priority."
The private check-in ("Flagship" in AA parlance) is in the same location in T4. It's restricted to:
- International or domestic 3-cabin first class passengers (currently that's JFK, HKG and LHR only, from LAX)
- Executive Platinum traveling internationally, in any cabin
- ConciergeKey
- Oneworld Emerald (not available within US, Canada, Mexico (except MEX), Bermuda, Bahamas or Caribbean)
- American Five Star Service customers (a paid service)
If your travels are not in one of those categories, the remaining premium check-in space is located adjacent to the Flagship entrance. If you're facing the Flagship room, that'd be the set of doors on your right (west).