Which specific airport/approach are you asking about?
At KJFK, for example, there are straight-in RNAV approaches to Rwy 22L and 22R, and a VOR approach to 22L with a 7 deg offset. It is clear from the charts and existence of the RNAV and ILS approaches that there are no obstacles to prevent maneuvering to final.
If there are no explicit restrictions on the chart, I would maneuver any time after the Final Approach Fix, so as to be on the runway centerline no later than the VDP (or constructive VDP of [MDH/300] miles, if not charted).
There is much discussion of straight-in approaches in Ch 5 of the FAA AIM, but no single, definitive answer.