Steve has got a good point. I'll admit I'm slightly tainted by the fact that I am not a Dubai fan at all and have been in Abu Dhabi for my entire 4.5 years in the UAE.
However, it's true that there are not so many compounds down here, but it is getting better and there are probably twice as many now if not more than there were in January 2011 and the expat community can be quite good in some of them. You won't find much in that regard in the real city centre, as that was built years before such considerations came into their minds.
Traffic can be bad in places, but if you find the right runs, which most seasoned AD expats can help you with then traffic can be easily gotten around. My wife does around 150km a day to do the school run, but in all honesty, the fact that the lowest speed limit (when you take that the speed limits are not the actual enforced limit*) is 50mph (80kph), it doesn't take long to get to most places.
On to schools. Get on with your search now! Depending on the ages of your kids, places are severely limited. The most popular schools have 10 applications to each available place, so you'll need to start applying immediately.
Things going on? Well, there's things going on all over the city to be honest. There are family places such as Yas Waterworld, Ferrari World, a whole host of family days at hotels, pool days and anything else you can think of. You can something to do most of the time, regardless of where you are.
Really shortstop, it's nice to say you want to live in a British expat community, but just get involved! There are loads of great guys and girls who are not british out here. I'm off out tonight to meet one of my Emirati friends who is a great chap. There's much to be found in this city and I'm sure if you're open minded, you'll love it. Don't hesitate to give me a shout if you need anything.
* All speed limits are +20kph, so in town it's 60kph on the signs, +20kph enforced (maximum) speed limit = 80kph. So 80 = 100, 100 = 120... Seriously, as you drive up the main highway to Dubai, the speed limit sign says 120, then 500 yards later, a larger sign says Maximum Speed Limit 140. Yes this is complicated and really reflects a brain bending level of logic that I've only ever seen in the middle east.
Also, if you think you've seen tailgating, local driving is Red-Arrows style formation flying. I hope you're not a nervous person.