Yes you can but you cannot do mountain biking you must stick to the paved paths
The trails that start at Quarry Hill connect all the way to the other side of town. The trees are pretty throughout the path and can quickly get to Silver Lake and other parks
There are paved trails through the park that are fine for bikes, but I wouldn't consider it to be a destination for biking except for very young children who don't travel very far.
You can bike on all the paved trails within the park, but they don't allow off trail, or mountain biking unpaved areas.
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