Of the 2, I would pick Harobur Island, because

Small island, can get around either golf cart, stiller or even walking
Gorgeous beach
Great restaurants
Actually has more to do than Eleuethera (although still pretty quiet)

Eleuthera, you need a car for everything. Long distances to other settlements, hard to find many beaches (although they are stunning).

BUT:

In your situation, I recommend another completely different island, Turks and Caicos because

Easy to get to on big jets (Eleuthera requires at least 2 places, with one being a puddle jumper, car rental, HI requires additional water taxi)

Most luxury condos, easy to keep staples for toddlers
Some extremely kid friendly beaches
A little shopping, but definitely much more than E or HI
A small casino
Lounge night live music with gorgeous settings (HI has some small bar/nightclubs for the rich and famous, E really only has Tippys close by)

TCI has the same gorgeous water that Bahamas has, and more to do

Don't get me wrong, HI and Eleuthera are stunning, bu t more off the beaten path, and beet for seasoned traveler.

TCI is much easier with a tiny one, it would be much more relaxing

Thanks!!

Agree completely with Blamona. W/baby in tow Turks is a lot more convinient. Both HI and Gov Harbour are difficult to get to...although once hooked you will want to keep exploring similar off the beaten path gems!!

Anywhere in particular you'd recommend we stay? Really want access to a beautiful beach with calm water. Thanks again!

Calm waters are never guaranteed! BUT, if you stay on Grace Bay, where the hub is and most resorts, etc, if the water is wavy, you can always go to Taylor Bay and Sapadilla Bay, which are a tolder's dream! Ankle to knee high super calm water, like a giant wading pool for hundreds of yards. (Car is required, although only 10 minutes away)

What's your budget? What are you looking for out of a place? Many resorts are condos with full kitchens, very convenient with babies!

oh, and to answer your other post about Virgin Gorda.

Nothing to Caribbean is direct from LA you'd have to go to Cabos or Cancun.

TCI (airport code PLS) is about as easy as it's going to get. Nice big jets, only an hour from Miami.

Most destinations are even farther from Miami, usually on small turbo props.

VG is stunning, you can get a flight to St. Thomas, then take a 2 hour ferry over to VG, or you can fly to Tortola, (usually a puddle jumper from either San Juan or Miami) then ferry over again.