Welcome to the forum !! The best place to stay for ya would be in the near of centre...but when you don't everything is very easy to reach with the dolmus-bus. Don't know when you are planning on comming but in season the drive of and on !! At night there are also lots of taxi's to get you home!!
When you have anymore questions, just ask there is always someone on here who knowes !!
I am sure you will have a great holiday in Kusadasi, like we all do
You wont have a problem with getting hotels for 10 nights, the problem you will have is with the flights.
most charter airlines (that the holiday companies run) only fly once a week to & from Izmir (the closest airport)
Scheduled airlines (Turkish airlines etc) fly every day, but the cost is a lot higher than the charter flights.
TBH any area of kusadasi is good. if you stay a little bit out of the town there is transportation (dolmus) that run every few mins until midnight, after midnight there are taxis that are really reasonable prices.
The centrum is where the majority of the nightlife is (bar street etc) but the other areas all have bars & restuarants that stay open late, so nightlife isnt a problem where ever you end up staying!!
I think its best to stay in centrum or out on Ladies beach, both areas r really great.
Ladies Beach is not that far away from centrum, but when u go back in the morning after u have been out partying, its best if u take a taxi
Claire is right, i think most charterairlines around europe does 1week or 2week, so if u only want to say for 10days u should probally go with turkish airlines.