I've lived in Chennai a few years ago when I was in my eleventh and twelfth grade and have lived in Delhi, Bangalore and Hyderabad in the past and have spent decent amounts of time in Bombay and Kolkota.
There are two-three great, pricey (by Indian standards) 'International' schools which I think you'll find suitable. Domestic Help will be easy to find and cheap as long as you get someone else from the city to handle the negotiating process. The usual standard for domestic work is that they pop in once in the morn and once in the evening in half and hour bursts and work pretty efficiently.
The night life
really sucks from a college POV but considering what you want there are plenty of great places where you can grab a cozy dinner + a beer. However, the night clubs are close to non-existent and there are only a handful of half-decent pubs. The scene is extremely safe though.
The safety is very high all-round too, I'm a bit nuts so it's routine for me to decide to take a walk at three or four in the night and there pretty much a 0% chance I'll run into a group of drunk douchebags throwing bottles around and **** which has happened a couple of times in Delhi. In fact safety wise, I'll rank it number one out of the cities I've lived for decent periods in. Still a good idea to make sure you live in a good residential area (one of three or four) for the comfort if not for the safety.
Obviously, like any Indian metro, there's massive pollution but it's not ****ing horrendous like Delhi/Kolkota/Bombay. The traffic is indeed an issue but again it's not a soul crushing rt of your day gone if you're unlucky like in B'lore or Delhi.
I lived literally a minute's walk away from a rugby ground and remember seeing some games going with a few expats in at least on the weekends. (Gandhinagar Rugby Ground) I don't really have any clarity on the matter though. Assuming Cricket/Football games would be easier to find with a few inquiries.
There are couple of beaches which are not rampantly overpopulated and still worth visiting. Sadly, the Marina is not one of them. The weather alternates between being ****ing hot in a thoroughly non-pleasant way to bat**** insane rains for a couple of months. At no point will the weather be chilly pleasant, not even in the middle of January. The auto rickshaws and the locals will try to rip you off your last belongings so getting a vehicle ASAP is absolutely essential. The schools will have school buses so that's not a worry. The public transport is dire and prepaid agency taxis are usually ****ing expensive over a longish term.
Frankly, It's not a city where I'd like to spend any part of my twenties in. It's not as spicy and diverse as Delh or Mumbai or as inviting and multicultural as Hyderabad or Bangalore but it's a very safe and stable place.
Let me know if you want to know anything else in particular.
and oh don't eat the Kaka Biryani in any of the hundred street stalls you encounter. It's flavoured crow meat rice and it tastes even worse than you'd expect.