What area of Madrid will suit us best?

[Sounbelievablydull]

We are going to Madrid for three days my sister myself and our daughters early twenties
We want to amble about some culture definitely shopping and eating!!
I have been looking At rental in malasana but not sure if this would be central enough.
We would really prefer to walk to as many places as possible
I'd be really grateful for some ideas as the flights are booked just need to sort the accommodation

La Latina is a young area with plenty of bars, restaurants.

Also areas off Gran Via which is very central. Hotel Suites Vienna well worth a look.

We stayed at 60 Balconies which is really near Atocha station. It wasn't a particularly hip area but it was incredibly close to main attractions and the apartments were immaculate. I think there are plenty of other options nearby.

Malasaña is central. It's the university area so there's a lot going on at night. It's nice but don't expect to have peace and quiet at night

That might be good for us then I'm not worried about peace and quiet there'll be enough of that when I'm dead!! Thanks for the replies x