Are monks allowed to travel during the rain retreat?
It's seven days and only if there is a reason, in a specific (but long) list of potential reasons, mostly pertaining to Buddhist practice. The only true exception I can think of to the rule is the case of obstacles to keeping the rains. As Thanissaro explains:


  Mv.III.9.1–Mv.III.11.13 gives a long list of valid obstacles, which Pv.VI.4 divides into 
  four sorts: dangers to life, dangers to the holy life, a threatened split in the Community, 
  and an actual split in the Community.
  
  http://www.accesstoinsight.org/lib/authors/thanissaro/bmc2.pdf