There's a wealth of ideas, but they need to be matched to your region, your target audience, and your budget.

One idea might be to invite local charitable organizations to do a free tabletop show on an annual or quarterly basis.

As Jay says, there are lots of ideas. For example, if you do a Google search on:
how to increase traffic to a mall

You can find quite a few ideas. Maybe one or more of them would be appropriate for you. Good luck.

You can use something called "PrecentPledge" it creates an in-sync system between the employer and employees who want to donate to trusted and approved charities, then you can see the results of your giving instantly. They work out of the same co-working space as my company does, so that's how I met them! They are a fairly new startup, but their service is solid, and a great way to go about corporate social responsibility.

Crème de la crème? Really? In Istanbul? I know the places as a visitor and as I stay at the Hilton International, I guess that I should match your target market. Though how you get corporate social responsibility whilst appealing to 0.03% of the population is beyond me. It is, however, a good idea.

Apart from the usual web things, which large malls and the 0.03% are into via their personal assistants, secretaries, butlers and mind coaches go for some on the ground stuff.

Partnership: What do the crème de la crème use, shop in and go to:
Set up some marketing alliances with:
All 4, 5 and 6-star hotels. Small exhibits and leaflets in their lobbies.
All luxury car dealers. Again small displays with takeaway cards.
Top Restaurants. Again, small displays with cards
The marinas on the Bosphorus: All the service and valeting points and go round the Yachts.
Private Jet charter companies: Same idea
Yacht Charter: Same thing
Night Clubs for the rich.
You get the idea -

Is your Mall well off enough to hand out Video Brochures? If so they are loved by the super-rich. They are already used to sell luxury cars, sporting events and even charity balls where they also double up as menu selectors by Wi-Fi.

Now for the social responsibility idea which will fill the mall and bring in new shops and sell some art and flood the place with the rich because at a fiesta they love to mix with the locals.

Before dong, all of these promotions and a web campaign, organize a party or a fiesta of art and music in the Mall. (Done this) All activity must lead to this date. And don't just do one. organize one, do about 6 over 3 months.

Now you need to invite a lot of locals.

I would not then go for Gazi Mahallesi and Karayollari or other such districts or your Mall will be in ashes. However, Central Istanbul has Many enclaves where the locals of all classes live. Target these people and invite them. You will know the areas a lot better than I do - I love eating in a transport cafe where there are no Europeans and only working locals. Those areas should be good. Pamphlet marketing for your fiesta should be the best approach as internet access and use is still poor.

Karakoy/Galata or the whole of Beyoglu would be a good starting point but you will know the best districts well.

Funny old thing. My family used to get people's art ventures going in the 1890's and 1910's by inviting a shed-full of aristocratic friends and then the whole of a lower-middle-class district to get the two mixing and enjoying themselves.

And they did. Your Crème de la crème targets will just love that.