Once you get to know your market, send your resumes during the "season" when theatres in your area do their hiring. In my area, that's usually around the same time that they announce their season (Jan-Mar).
When I do a mass mailing of resumes, I usually make a list of all the places that I would really want to work. Then, I try and do 3 or 4 a day until I get through the list. That way it doesn't become a totally unmanageable project.
I recommend keeping some kind of record of your communication with these companies. I have a spreadsheet- I keep track of when I sent a resume, who I sent it to, if I got a response, if I had an interview, if I got hired. It's easy to remember who I've contacted before, and which mailings have been the most successful.