The water all around PR is clear and "blue", but it is the sand underneath that makes it have that "Caribbean blue water" look. White sand is what you are looking for.
What else (if anything) do you want to do besides look at water? That will help decide.
I love Culebra, but it is VERY low key (dead after 8-9pm). But beautiful water/beaches.
Vieques is a little more active, also lots of beautiful beaches, and some on land tourism to do but it is a small island.
Cabo Rojo has some amazing beaches with the water you want, and you have the whole main island full of activities to explore and almost every type of activity from casinos to zip lines.
Balneario La Monserrate in Luquillo
Icacos beach - $25 per person roundtrip by water taxi
Culebra Island - $4.50 per person roundtrip by ferry
Vieques Island -$4.50 per person roundtrip by ferry
Pena Blanca Beach in Aguadilla
Crash boat beach in Aguadilla
Buye Beach in Cabo Rojo
Playa Sucia in Cabo Rojo
None of the above, I would take a water taxi to Icacos that you can reserve ahead of time. That would be the easiest option. Otherwise, take the ferry to Culebra, but be warned that July is the most popular month of the year for locals going to the beach, so the ferry will be full. If trying the ferry, go on a weekday and arrive early. Tickets are not sold ahead of time.
I would suggest to take a Catamaran trip to Icacos Island instead of Water Taxi. On a Catamaran you have a Crew to take care of you, serve Lunch and drinks, shade on board , Bathroom and provide snorkel gear. Otherwise with Water Taxi you'll need to bring cooler, gear, and are stuck in the sun till they pick you up again. Icacos is deserted, so what you need you have to bring.
you can take ferry or a tour to culebra i would check out flamenco beach one of the most beautiful beaches I've ever seen.
here is link to video
starts at 1400 minute mark.
It’s due to budget/logistics, not being afraid of the flight.
Do you recommend a certain catamaran trip company?