Correction on my post: it's ESPN CLUB, not Zone. You have a few options on how to get there:
1. Take a bus to one of the parks (I suggest the one closest to your resort), and then hop on the BOARDWALK/"whatever resort is its partner" bus.
2. Take a taxi from your resort to the Boardwalk Inn.
3. Hop on the DTD bus from your resort, and THEN another bus over to the Boardwalk Inn.
4. If you happen to be at EP or DHS, you could walk over. From EP, exit out the International Gates and make a right over the bridge. And from DHS, follow the signs to "Boardwalk;" then cut past the pool, thru the 'tunnel,' past the Art shop, and you'll find yourself literally on the Boardwalk (just ask a CM at the pool for directions).
Once you get to the resort (if you take the resort bus route vs. walking over from EP or DHS), simply ask a CM to direct you to 'the Boardwalk.' The ESPN CLUB is located toward the Beach Club resort and EP along the Boardwalk...you can't miss it. Arrive early, because it will be busy (bearing in mind a 6:30 p.m. EST kick-off)!
To get back to where you need to go, simply walk back to the Boardwalk Bus Depot (ask a CM if you forget the way, because the resort itself is somewhat of a maze), then hop on the DTD bus (although MK is slated to have Evening Extra Magic Hours that night, I'm not sure if WDW implemented the 2-hour evening limit yet, which would have MK closing at 10 p.m. instead of 11 p.m.). From DTD of course you could pick up your resort bus.
If all that sounds too complicated, you could simply get a taxi from the Boardwalk Inn back to your resort. I don't know prices though.
The Boardwalk is quite the lively place at night, so your family definitely will not be bored!