Hi Dina,
Congratulations on your anniversary! Vieques is a great place to celebrate. Plus the W is very nice.

You absolutely have to see the bio bay. It is pure magic. Even if that's the only thing you do on the island, nothing else will compare. Make sure that you go with a company that has the transparent kayaks.

There are many nice beaches on Vieques, but you don't need to see them all. if you have a car for one day, the hotel can pack you a picnic lunch, and you can drive and visit 2-3 beaches for a very nice day out. You can also rent some snorkeling gear to take with you to some of the beaches. We did something similar and visited the beaches on the south side- I remember Pata Prieta was nice, but really they all were. They're all close by so if you just drive to that area you can sample several of the beaches and settle in one that you like the most.
We unfortunately decided to do this tour with bicycles, not realizing that to get to the south side we'd have to climb up a tall hill. Well, we got to the beaches completely exhausted, and on our way back it was already getting dark and we had to call the hotel to send a van to pick us up. Quite a day that was.

Re Esperanza - yes, there are shuttles/taxis from the W. it takes less than 30 minutes, and they will come pick you up to go back, so no problems trying different restaurants on different nights. I remember being to El Quenepo and having good food, but it wasn't all that incredible. It was good, but pricey and our service was ok-ish. We often ended up eating at the W along with our drinks by the pool or the beach. It was a great time!

We have been researching PR and things to see and do. I found this moon calendar that shows the best dates for the Bio Bay tour. Hope it helps with your planning.

http://www.puertoricodaytrips.com/biobay-and-moon/#mooncalendar

We spent four days on Vieques last summer, but stayed in Esperanza and went over to the W only for lunch one day. As olionin said, the bio-bay tour is a must! We explored many, many beaches with our three children and found that Caracas beach was our favorite. We very much enjoyed dinner at El Quenepo. It had a very romantic and authentic atmosphere.

Thanks everyone for your helpful replies!