As others have said, Boma is a buffet.
We have dined at all three of your choices, and also Jiko.
Seeing as how Jiko is signature, it may not be what you're looking for either.
Boma is relaxed, a bit more noisy than the others due to the number of people, however, IMO, it's the best for young children. No one bats and eye at kids bouncing here and there at boma. We've dined there several times for different meals and enjoyed each time, the food selections were nice, but nothing overly different.
Sanna has a lot going for it. We love the theme, the ambiance. The food, when it arrives, is delicious. My children (ages 2, 4, and 6) all enjoyed their meals, as much as they were able given the way our night ended up. I LOVED the tandoori chicken, I don't actually recall off the top of my head all we tried, but it was all very nice.
One concern we had, which was important when dining with young children, we arrived early, about 30 min early. We should have been one of the first seated since we had an early reservation. However we were 1.5 hours late being seated (2 hours waiting for a table with littles). We enjoyed the animals for the first 30 minutes, then managed to keep them occupied for another 15 before the whinging started. By the time we sat down I'd had to run to pick up a bottle for milk for my toddler who likes milk at bedtime. Had to run and buy snacks for my bigger kids, and by the time we were seated my toddler was asleep in my arms. We were there right at open and they were very late.
My other concern with Sanaa is that we have strict dietary restrictions, noted on reservation, spoke with the waitress, and manager before ordering (this is one of the few restaurants the chef did not speak to us). They made several mistakes with our (children's) meals twice bringing stuff to our table that was not safe. The one time we questioned it and the waitress argued with us telling us it WAS safe. We chose not to allow our children to eat it anyhow - and with good reason. About half way through the meal the waitress returned red in the face when the chef realized she'd brought the wrong food to us. Our children were tired and hungry and never did get to eat their full meals, we were offered no compensation.
It may not be significant to everyone, but to me it really sours an experience to end up needing 2 hours for a meal (plus 2 hours waiting), and still leaving without half your food, paying full price, and ending up with grumpy, hungry children.
We've had issues with other restaurants bringing unsafe food, but most bend over backwards to make it right. Raglan road made a mistake once and comped our entire meal, as well as having managers, chefs, waitstaff, dancers etc all come and make sure my DD was okay.
Kouzzina was very nice, we've dined there a few times since they opened. I love their fisherman's stew. DH orders the lamb almost every time. Our children enjoyed the food and the staff are friendly. We always enjoy a stroll down boardwalk after our meal.
In short, I'd say kouzzina. Enjoy a flight of their greek wines. A perfect way to round out the day.