A good time to look is the month before each quarter. Another is summer if you plan to live in Claremont then.
Early summer is when the best deals are available.
Demand peaks in September, when students and faculty arrive in town and vie for the best housing deals. Plan to spend 15-40 hours looking for a place to live. This time can be compressed into one hectic week or spread out over a month. The latter allows you to find the better bargains. Study the difference in housing costs.