Have 2 kids.
Eldest is not the most active naturally but loves healthy food. Balance and a taste for yummy veges has been instilled since day one. He loves junk food too but
chooses to eat fruit n veges - speshly if he has had some junk in the day. Good thing as eldest lad has a low-ish metabolism and can get a bit pot-bellied if not active for a few weeks.
Youngest couldn't be more diff. Total meatasuarus and reluctantly eats veges (last). Ok with fruit but is always snacking (tempted to lock pantry to halt the sneaky little bugger) and "not hungry" at meal times. Have laid down the law on finishing breaky and eating dinner veg or look out. He is skinny as a toothpick and SUPER active.
Go figure

Reluctantly I introduced the kids to a 2nd hand original X-box a couple of years ago. I'm not a gamer as such and was keen to hold out as long as poss. Eldest was 6 at the time and to be honest i felt sorry that he was such a gumby and out of step with other kids/peers. No one wants to be the kid wearing sandles and socks - know what i mean?

(speaking from experiance here

)
Anyway have had 2 breakthroughs for keeping em active.
Took both to skate park for 1st time the other day. Awesome. He loves swimming but has never been big on ball sports nor running etc, yet Eldest was ragged and knackered but trying to keep going at the end.

Begging to come back next day. Which we did.

2nd breakthrough. Bought an X-box 360 with Kinect. Totally cool and at last a truly
active video game. Some of the 'Adventures' games that ship with it are kn awesome workouts and all in the name of fun. Sure you don't want it to replace the idea of getting outdoors and keeping fit/active but it is a bloody good option for winter/busy times and just for fun for them HIGHLY recommended.
Balance is easier to say than achieve in the busy world these days. If you can get some decent nutrition into em
daily and find the activity that works
for your kids then you are on the right path.