Thanks to the Seattle Public Library, with your library card number and pin you can get free admission to participating Seattle Museums. Luckily Woodland Park Zoo is on the list. But I would highly recommend visiting the zoo even if you had to pay for it.
The zoo’s website will give you all the info you need about how to get there, and the price of parking. There is also free parking nearby in the residential streets.
Woodland Park Zoo is huge. Plan to spend the whole day there, or at least half of the day. And you probably won’t get to see everything even then (especially with kids). You are welcome to bring in food and there are plenty of places to sit and eat.
There is a beautiful classic carousel that is 100 years old with hand-carved horses. It can be ridden for an additional $3 per person.
The zoo is very well maintained, clean, and up-to-date. We’ve been on a Sunday in July and even then it did not seem crowded (although the parking lot was full – but we easily found free parking nearby).