Find 2386 flexible and convenient short-term apartments for rent in San Jose. You need to find a landlord that has flexible leasing available, or month to month leasing available.Visit the property website from a desktop computer, laptop, or smartphone and select Lease Now to begin the application process. Maintenance. How many short-term apartments are available for rent in San Jose? To end a month to month lease in California, of you pay your rent monthly, you must give notice of 30 days. (If you pay weekly, the notice is 7 days). California landlords can collect security deposits up to 2 months' rent for unfurnished units and 3 months' for furnished. Look at your rental agreement. In general, it becomes month to month if they don't ask you to resign a new lease. Discover San Jose, CA's largest selection of weekly rentals with cozycozy.