Why do some military jets have needle-like structures at the nose and others don't?
What you see on the SR-71 is an Alpha-Beta probe, with a pitot tube branching off the side of it. The nose cone of the SR-71 (and its variants) were changeable depending on its loadout.

From the A12 Configuration:


  The sharply tapered nose section was pressurized and contained navigational and communications equipment, a
  remote compass transmitter, periscope optics, air inlet computer and angle transducer, and other radio equipment.
  A combination pitot-static and alpha-beta probe was installed at the forward tip to capture airspeed and altitude data.


About the SR-71 versatility


  The SR-71 also served as a testbed for an Optical Air Data System (OADS), a fiber optic device using laser
  technology to replace the pitot tube (airspeed probe) on high-performance aircraft. It used laser light instead of air
  pressure to produce airspeed and attitude reference data such as angle of attack and sideslip normally obtained with
  small tubes and vanes extending into the air stream or from tubes


Both sources above: Design and Development of the Blackbird

The F22 serves quite a different purpose to the variants of the Blackbird, and thus probably has less need for sensitive sensor equipment of the SR-71. It still has a pitot tube which can be seen in the photo you posted



And it, no doubt gets other avionic information from a traditional pitot-static system rather than rely on an alpha-beta probe as the Blackbird did.