I would say it is a bit further than 2km, more like 4 or 5, but if you keep going along the coast road, after Koca Calis/Ciflik beach you cross behind a small headland, the next beach after that headland is Kargi beach. There is a small charge to drive on to there in the summer but free if you are walking. The beach itself is long, mainly pebble, quite and undeveloped with a smaller cove beach at the start. There is also one small restaurant, just at the start of the main beach.
Well worth a look if you fancy a change of scene, it's worth noting that the area can get quite busy on weekends when loads of local families arrive for BBQ's and picnics.