Writeable and Executable location on Android
/data/local/tmp/ and "/data/data/" + packageName + "/files"
for direct testing you target binary , first is recommend.
If you can use adb, you can prepare directory /data/local/bin with 777 permissions.
Alternatively, you can create a file in the private app directory (/data/data/your.package.unique.name/files), and set the file permissions to 777 755.
If you want to avoid rooting the device then basically SD card is the only place you can assume is world writeable
EDIT: mind recent changes in Android framework as of 2014/2015!.
It's better to make your binary part of installable APK which then extract this binary out of APK into private storage, make it world executable etc and somehow announce binary location, but in general expect some problems depending on OS version and vendor