I would say between April to before end of November. If you don't mind summer temperature, then June or August is good too although this would be the peak time where most visitors (hundreds) come, due to school summer vacaton time, which makes the parking quite challenging, unless you come using an uber or a lyft. if you drive come as early as 8.45 a.m. and leave before five p.m. Why don't you try it in the middle of April. You may spend the whole day (from early morning on 15th April) at the Fairmount Park where the Subaru Cherry Blossom Festival is held (once a year only) then go to the Zoo a day before, or the day after. My own best time to take my kids and go to the zoo is always Monday; not on Saturday and neither on Sunday, and of course you know why.
Early in the day as the animals are more active.
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