Depends what your budget is really.
The Marina/JBR is cool if you want to be close to restaurants, bars, the beach etc but it’s busy and noisy almost 24/7 (I say that as someone who lived in JBR for 8 years)
If you’re looking for suburbia, then Arabian Ranches 1 and 2 are a good option. AR1 is older, greener and some of the homes have private pools) Both have small community centers with supermarkets, nail salons, pharmacies etc. AR1 also has a golf club if that’s your thing.
Dubai Hills is also a new and increasingly popular community. Decent central location, modern and spacious villas and also a very nice golf club (with restaurants/bars) As it’s so new it’s not very green yet and there’s still quite a bit of construction going on.
Otherwise there’s Jumeirah 1/2/3 - much older villas that have a very different feel to a lot of the rest of Dubai. Some will have private pools although as they aren’t in gated communities as such, you won’t have things like a Carrefour or Spinneys on your doorstep.
Downtown is another area worth considering if you’re after trendy, urban living. Lots going on there - bars, restaurants, the opera house, Dubai Mall etc. I have small kids so for me it’s too busy/noisy but I have lots of single/childless friends who have cool loft style apartments there.