Your understanding of Florida law is inaccurate. The LL has 15 days to return your full deposit OR 30 days to send, by certified mail to the Tenant's last known mailing address, a notice of intent to claim part or all of the sec dep. The tenant then has 15 days to respond by certified mail indicating the Tenant's objection. If the Tenant does not object, the LL may deduct the amount claimed and forward the remainder to the Tenant (within 30 days of the Notice of Intent).
Regarding whether you can sue in NY is a question to be asked of NY attorneys, but as the LL lives in PA and the contract arose in FL, it would appear that NY courts have no grounds for jurisdiction.
If you believe the LL wrongfully withheld funds from your sec dep, you will likely have to file in Florida. You will need to weigh the costs of doing so vs. What was withheld.
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