If you have a 'United States Alien Registration Card' then you can stay for no more the 30 days.
Besides Puerto Rico you can visit the US Virgin islands without a visa. All other islands, you will have to check as entry requirements vary.
As a Lebanese citizen, you will need a visa to enter the Bahamas.
However, you do not specify what kind of US visa you have, but if you hold a US alien registration card, you may travel to the Bahamas with your Lebanese passport and the US alien registration card and work permit or residence permit for stays of up to 30 days without getting a Bahamian visa. In all other instances, you will need a Bahamian visa.
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