You may wish to consider three options for your few days here.
Alaçatı had transformed itself over the past 10 years or so from a village of crumbling former-Greek houses to a ‘Boutique Village’ with an international wind-surfing centre. It’s an attractive town with pavement cafes, etc. but it would be difficult to find accommodation or restaurants at what I would describe as reasonable prices. Maybe not impossible with food, but nevertheless extremely difficult. There is a new marina and a couple of night clubs close to the beach, just 4 kilometre from the town
Çeşme, offers a huge choice of hotels, restaurants and bars to suit all tastes and pockets. The night clubs are a few kilometres away, mainly at Ayayorgi Bay. The town still retains very much of a Turkish atmosphere with the Genoese Castle and the maze of streets behind.
There’s Ilıca, too, which has a long, pale sand beach with warmer-than-usual sea as a result of underwater thermal activity and a good choice of beach bars/restaurants. There is an excellent choice of restaurants in the town and hotels ranging from five-star to pansiyons. But it’s really a one-street town and, in my view lacks character or atmosphere of both Çeşme or Alaçatı.
Car hire is not essential as the three towns, and beaches, are easily accessible and linked by Dolmuş, the inexpensive shared mini bus service. Also a 15 minute journey from Çeşme would take you through the village of Çiftlikköy (where we live) to probably one of the best stretches of sand on the Aegean coast (Altınkum Beach) and Pırlantı (Kitesurf) Beach.
The following link may help you with accommodation: http://www.cesme.gen.tr/Default.aspx
I am sure wherever you decide, you will have a most enjoyable stay in this lovely part of the Cesme Peninsula. Your final choice will depend on your preferences – and your budget!
Do let me know if I can help further.