Best way to get from Beşkitaş to Ataturk airport?

Hello everyone

I am leavıng for a small holıday to Hungary tomorrow. I lıve  ın a very crowed resıdental neıghbourhood wıth seemıngly no access to the metro (my closest statıon ıs Levent no?) so I am wonderıng what ıs the most economıcal way to get there. I do not quıte understand the bus system yet.

I am a lıttle afraıd of how much ıt mıght cost to go by taxı :(

Thank you :)

I suggest go to Zincirlikuyu via bus or walk, then metrobus to Zeytinburnu , then change to Airport metro. This is fastest but not cheapest.

I would suggest other way. You go with a bus or dolmuş to Taksim and then you get 96T directly to the airport. 96T takes around 40 min to arrive there. I don't think you can find cheaper. Here is the schedule of 96T:
iett.gov.tr/en/saat/hareketsaati.php?hid=saat&hat=96T&a=q

you can go to Taksim square by underground for 1.75 lira then there is a road from taksim square  towards osmanbay, nisantasi, levent... which airport buses stop. they called Havas , they take you directly to Ataturk airport for 10 lira .. this is the best and most comfortable way.. they are airports shuttle buses.. just be careful dont get to the one for Sabiha airport., here is the link for time table,
ataturkairport.com/en-EN/Transportation/havasbus/Pages/hoursservice.aspx

As Midoo wrote the best & cheapest suggestion. I will go with him. Ask anybody for Taxsim Dolmus from Besiktas. Yellow color van pool in taxi. It will take 2.20 Tl to Taxsim & 96T bus is every half an hour to Airport which will take you right inside the airport. If you have a luggage trust me underground metro will be very painful, specially coming out from taxsim stop.

I hope this helps.