A kids area targeted at ages 2-10 is certainly a great feature. I'd vote for away from the food area for a few reasons, mostly that it tends to reduce the kids "playing" with the food, and allows travellers without kids better access to food. A few basic toys, a "cubby house" (not elevated just a little house - there's lots around that are made of plastic - so easy to clean!) - that sort of thing. Older kids thAt use computers etc unaided these days tend to have their own. The trick also with the kids space is not to make it too small so they have room to run - making everyone's life easier both on the ground and in the air.
You also want to encourage the kids to be supervised, so tucking it too hidden, whilst advantageous for noise for the rest of the lounge, risks (when it's busy) kids being inadequately supervised. Ideally you want an area with seating around so the parents / older kids can sit and relax whilst the toddler age kids can play (with "distant" supervision). I hope that makes sense.
When you use kerbside entry in sydney, you go through security and then enter to the right - there is the area immediately to the left when you enter - that would be a good space IMO.
Re: rooms. Multi purpose is best. As Princess Fiona comments, she tends to use them for family space / privacy. So segmenting areas off for "private use" as opposed to purely branding as "meeting room" would be better. Ideally the ability to reconfigure the room would be useful.