Who checks the instruments and avionics before the crew boards an aircraft?
In general, nobody else does.

When pilots arrive to an aircraft for the first flight of the day, extra checks are performed by the crew to verify aircraft systems are all working properly.  These checks are done once per day and subsequent flights will perform abbreviated checks instead.  A visual walk around inspection is accomplished before and after every flight. 

Maintenance will check on airplanes at required intervals but outside of specific checks (associated with the carriers approved maintenance program) the only time they'll check something like a pitot tube is if the crew notes a problem and writes it up.  At that point maintenance will address the issue to return the aircraft to airworthiness.