QUESTION:  Are there times of the year (locations in earth's orbit) that are
better or safer for making observation's from the HST?

ANSWER from Jeffrey Hayes on April 30, 1996:

For the question on whether there are spots in the orbit that are best for HST 
observations, the quick answer is no.  HST is (or tries to observe) 24hrs
a day all year 'round.  There are times when specific objects cannnot
be observed because they are too near the Sun, or the Earth's limb, or
the moon, but the telescope is always being used.  This is unlike ground-based
observatories where one usually observes only at night when clear out.  
One of the major reasons for building and launching HST was to break the
day/night cycle (and also for resolution).

Cheers -- Jeffrey