Park is open from sunrise to dusk. Visitor center 9-5, Washington's headquarters 11-5, trolley tours 11,1 and 3 (fee for the trolley). The rest of the park is free.
The park also has a website with all kinds of useful information that can answer any questions you have. Like Beth said in her response to your question, the park is open from sunrise to sunset. The Visitor Center is open from 9:00 am - 5:00 pm. There is free parking and a lot to see. If you have internet access it would be beneficial to check it out. The best time to go is really personal for each but the website will give any events that may be going on to help you decide what works with your schedule
It depends on weather
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