Çeşme is a district of İzmir and located on the peninsula that is west to the city. Although it is a small district it becomes very crowded during high season (middle of June - end of August).
Çeşme can be reached from the ADB airport, the airport is close to the center of İzmir and it is around 100 kms from Çeşme.
If you are coming with a transfer from İstanbul and you have a checked-in luggage, beware that you should pick up your luggage from the 'international flights' terminal. What usually happens is they leave you at one of the gates of the 'domestic flights' terminal and then you need to walk (the distance is not much) to the 'international flights' terminal. There information that they give you is, when you walk towards the exit there is someone you yells about this (in Turkish and in English)... very efficient :P
You can reach to Çeşme from the airport:
One important point about the highways is, you cannot pay by cards or cash (this doesn't make any sense but it is how it is), so ask for a HGS (which is short for 'Hızlı Geçiş Sistemi' 'Fast Passing System') sticker from the agency. I think all rental cars have this sticker, but check with the agency.
A typical toll gate. 'KGS' is not used anymore. Depending on whether you have 'OGS' or 'HGS' you need to use that (most probably the rental cars would have HGS). You need to pass very slowly 20-25 km/h, otherwise the gate may not scan the sticker on the window. There is no toll gate on the İzmir side (the airport side), therefore you will only pass from a toll gate when exiting from Çeşme.
The route:
You have 2 options to move around Çeşme:
The first stop from Çeşme in the direction of Ilıca and Alaçatı is here: https://www.google.it/maps/dir//38.3259673,26.3087809/@38.3264071,26.3080487,19z/data=!4m2!4m1!3e2
The wind usually blows from North or North-west direction, therefore if it is windy northern beaches are usually wavy.
https://www.google.es/maps/place/Sakarya+Mahallesi,+Ayayorgi+Yolu,+35930+%C3%87e%C5%9Fme%2F%C4%B0zmir,+Turkey/@38.3385064,26.3078165,17z/data=!3m1!4b1!4m5!3m4!1s0x14bb7a3da562ecab:0x99aa1e79f8e7c54f!8m2!3d38.3385064!4d26.3100052
https://www.google.com/maps/place/%C3%87ark+Plaj%C4%B1/@38.2470416,26.3824929,17z/data=!4m13!1m7!3m6!1s0x14bb786d91f599ff:0x3a174cff22005d88!2zQWxhw6dhdMSxIEJlbGVkaXllc2ksIDM1OTMwIMOHZcWfbWUvxLB6bWlyLCBUdXJrZXk!3b1!8m2!3d38.2728757!4d26.3839765!3m4!1s0x14bb7f234298b43b:0x7cf142c40bb96221!8m2!3d38.2463653!4d26.3835577
https://www.google.com/maps/place/Alt%C4%B1nkum+Halk+Plaj%C4%B1/@38.2670081,26.2321353,14z/data=!4m12!1m6!3m5!1s0x14bb7cec639cd8d1:0x3cba47a1788e5fef!2sAltinkum+Beach!8m2!3d38.2703703!4d26.2594724!3m4!1s0x0:0xca994d71613295ac!8m2!3d38.2681864!4d26.2741041
They are around 8 hours of tour with lunch served on board. They go to these places as far as I know:
There is the old marina where boat tours can be found (see that section); good for night time walking. Also there is the new marina where some shops and restaurants/bars can be found. https://www.google.it/maps/dir//38.3204455,26.3027141/@38.3215692,26.2992916,17z/data=!4m2!4m1!3e0
There are ferries going to Chios everyday from the port. It takes 45 minutes. You can buy the tickets at: http://www.erturk.com.tr/en You do not need to buy in advance I think you can even buy the ticket that morning from their shop. The port is here: https://www.google.it/maps/search/ulusoy+port+cesme/@38.3222976,26.294866,17z/data=!3m1!4b1
If you are are going to spend a night there you can visit Kuşadası (another coastal town) and Şirince https://en.wikipedia.org/wiki/%C5%9Eirince
And you can see the see side, there are restaurants and bars there. https://www.google.com/maps/dir/38.4297697,27.1343529/38.4413705,27.1427117/@38.4405806,27.1431409,16z/data=!4m2!4m1!3e2
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