1. It is a good act to run to the synagogue, as indeed to any other holy act (or fulfilment of any commandment etc.). Even on Shabbos when it is forbidden to take steps which are too large, one may run to the synagogue or to perform any other holy act. It is obvious from the above that one must also be especially careful when walking to the synagogue not to stop on the way or to have a wasteful conversation with a friend. (Shulchan Aruch and Mishne Berurah 90)
2. Inside the synagogue itself one may not run. Instead, one must tread with awe. When one leaves the synagogue one may not run for it appears as if one is fleeing from the synagogue. An exception to this is if one is going to the study hall to learn Torah or when is leaving the synagogue to do something quickly and return immediately, when one is allowed to run in order to facilitate a quicker return. (ibid)
