It's shorter distance wise from Fajardo. Yes, it is safe to go to El Yunque on your own. It is part of the United States park system. What are you afraid of wild animals? Crime? There are no wild animals and crime is very rare. It's best to go to Vieques for at least 2 nights to really make it worth while. If you only want to do a day trip, it's best to go to Culebra.
Echo what @prexplorer says.
Only thing to add - get to El Yunque early to avoid the crowds and enjoy the trails
And really echo what @visit-the-coqui says - get there early & try to avoid a weekend - it gets really busy!!!
Going to be there in 3 weeks. How will the crowds be during the week in September? How early is early?
The reason one should get there early is to secure a parking space for a rental car. Spaces are limited.
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