DeMarco

My family is looking to visit the Caribbean (open to any island that fits requirements) around June 21, 2018. Looking for an island with non stop flights from Philadelphia or Newark.

Here is what we’re looking for:
1) Family friendly resort, preferably all inclusive. My daughter is 8 and I would love for her to have other kids to play with but would like to stay away from ‘disney’ type resorts!
2) Great snorkeling on hotel premises. This is a must for my husband!
3) Budget between $3-$5K.
4) Private beach, nice pool and relaxing.

any recommendations would be greatly appreciated!

Odin

Grand Cayman has snorkelling just off hotel premises but does not have AI hotels and neither do you need one there. Also pretty expensive.
Cozumel has AI hotels with snorkelling off hotel premises but some hotels do not have a beach let alone a private one, Also, need transfer from Cancun to PDC and ferry over to Cozumel. For snorkelling you need rocky beaches. There might be other areas eg Riviera Maya that offer all you seek.
St Lucia has snorkelling off some beaches eg Anse Chastenet Hotel, beach is not private to the hotel, beach is dark sand which I find very beautiful. AI is available at this hotel. No idea if this fits in your budget.
Antigua has several beautiful beaches, none of which are private to hotels, several AI hotels, snorkelling off hotel might be possible.
Aruba has snorkelling but no need for AI hotels as there are many restaurant choices.
I'm going to T&C for the 1st time in a couple of months so can't comment on snorkelling there but fully expect to travel away from or to another part of Grace Bay to find good snorkelling. I believe there is only one AI.
Bermuda has fantastic beaches, great snorkelling, some right off hotel premises, no AI hotels to my knowledge (or very few) and an expensive island
Jamaica's snorkelling is not great but has wonderful beaches and hotels, many of them AI.

RoamsAround

Beaches Resort on Providenciales' Grace Bay (Turks & Caicos) is an All Inclusive that caters to families (your daughter will have plenty of playmates in her age group) but it's on the pricey side and because of it's size may meet your definition of a "Disney style" resort. There's some good walk-in snorkeling on Grace Bay but not necessarily right in front of the resort. I believe there are a couple of non-stop flights from Newark - not sure about Philadelphia.

There are lots of "condo resorts" on Grace Bay that are very popular with families so odds are good your daughter will find playmates. You'll find the price points lower than at Beaches. Again, snorkeling is available but not necessarily right in front of the resort.