I have read the the best reef snorkeling from shore is near Coral Gardens - Correct? If so, what hotels are in easy walking distance from the shore where one would enter.

Thank you.

Coral Gardens Hotel, Sibonne Hotel, Alexandra Resort, Beaches, The Sands

About 15 min walk from Beaches--25-30 min from the others mentioned. Also Turks and Caicos Club about 5 min

Superb snorkeling and easy enough for novice swimmers.
It can be a demanding walk from places like The Sands due to heat -- if you do walk it just make sure to drink plenty of fluids.
From The Sands it is a good 1/2 hour walk and from OCW 45-60 minutes. We have stayed at both and done the walk.
Enjoy!

Turks and Caicos Club is next to the reef. We just stayed there.

We were disappointed in the snorkeling at Coral Gardens, because so much fo the coral has been damages. The best place on the island to snorkel, bar none, is Smith's Reef. You will need a car, or get a taxi to drop you off and come back and get you.