Thing to do from Hollywood to Key west Florida
I'll go ahead and assume you're talking Hollywood, FL.
If you like out of the way, dive-ish places, stop at Alabama Jacks on Card Sound Road. Right before US 1 goes towards Key Largo in Florida City, you're presented with an option to take Card Sound Road, there is a $2 toll bridge involved but, I think it's well worth it.
Alabama Jacks is right on the water, and they have drinks, food, and sometimes live music.
They have the BEST conch fritters in the keys.
Hope you have a good trip.
Assuming Hollywood Florida as that is in the title (which I couldn't see at first) and not Hollywood California.
If you start at Hollywood Beach you can drive down along the Atlantic on A1A - you will have the Intercoastal Waterway a few blocks away on the west side. When you get to North Miami Beach you will cross the bridge at Haulover Park You can go all the way down to Miami Beach before you have to cross over to the mainland in Miami. I'd try to stay off of the expressways around Miami unless you have a car with a transponder because some of them are toll roads which only collect electronic tolls - you can't pay cash to a toll taker. As you proceed down through Miami (Miami attractions could be a whole 'nother topic) and Coral Gables go to the Everglades, going in at least as far as the Anhinga Trail
You have a choice at the top of the Keys - either to take US1 the whole way or take the toll road (less traffic) to North Key Largo There are a bunch of state parks in Key Largo - including Key Largo Hammock State Botanical Site, and John Pennekamp Coral Reef State Park (which is under water)
From here it is just a straight shot down US1 to Key West - passing Marathon where you can go fishing, or snorkel or dive at Sombrero Key, look at Boot Key Harbor where all the cruising boats anchor, or visit the Crane Point Museum and Nature Center, and Pigeon Key before going across 7 mile bridge. When you get to Big Pine you can visit the Blue Hole Observation Platform to see alligators, looking for the Key Deer or possibly going to the weekend flea market there. And you shouldn't miss the Bahia Honda State Park which has probably the best beach in the Keys
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Very broad question. Are you driving straight through? Planning on stopping and staying along the way? Can you provide more specifics?