We just got back from a BWV and VB trip with 3 kids (DS-9, DD-5, DS-2.)
There is a Publix where noted by jimminarik. The liquor store is also still there in that strip along with a Chinese food place, a Subway, and a couple other places
Activities the 5 days we were there included:
Scuba Diving Lessons in Pool -- ages 12 and up I believe
Catch and Release Fishing -- might have been 7 & up
Archery -- 9 and up I think
Snorkeling Lesson in Pool -- can't remember min. age...maybe 7
Turtle Walk -- need to be drawn from lottery to participate; min.
age was 7
CampFire -- Family activity
Unbirthday Party -- ages 4-10 (get to Ebb and Flo's before 9 a.m.
the day of the party to sign-up as it fills up quickly)
Underwater Fish Hunt in the Pool -- any age.....basically the CMs
just throw handfuls of fish in for kids to retrieve; only lasts
about 10 min. but the kids liked it
Lots of activities for 3-5 year olds but 2 year olds can participate
if interested with a parent's help--they don't check ids!

Examples include Fish Hunt (for toy fish in main lobby, Mask/Crown making followed by tea-party and parade, treasure hunt near the pool.)
My DS (9) spent a ton of time in the arcade....unfortunately that did cost me, but he enjoyed his independence and it was right by the pool.
There's also a mini golf course right by the pool that the 9 year old and 2 year old (he's almost 3) did too many times to count.
The pool itself has a great slide, and they rent boogie boards at the end of the boardwalk to the ocean which seemed to be a favorite activity for many pre-teen boys.
Finally, based on the recos provided on this board, we went to the Green Cabin room which looks just like a bar, but the entertainers they had in the evening really catered to and involved the kids. All the kids were up and dancing, we did a conga line, etc. We had a drink; the kids all got milkshakes and thought it was great.