We stayed at the LA QUINTA Hollywood property last December. Booked again for this December's cruise.
Stayed ONE night, and able to park for the duration of our 10 day cruise.
Google the property.
Check the rates on the internet.
THEN, call the property directly to confirm that you can park for free. They'll probably not be able to match the internet rate on the La Quinta site, but at least you'll confirm they still allow free parking.
They have a free shuttle TO Port Everglades, but you're on your own on the way back.
We parked in front of the property under a streetlight, and had no worries.
Nice property. A couple of dining options within a walk's distance. (Don't know how old your folks are, but it would be an EASY drive, off of the main roads)