I have a clog in my bathroom I ran a hundred ft snake down the toilet. I still have standing water in the bottom of the pipe. I have city sewer. The house was built in 1964 so I don't know if it has a cleanout. So my question is should I have standing water if there is no clean out?

Where is the "standing " water? Bottom of what pipe? Running a snake down the toilet may do nothing if the clog is in the drain line.