Could not identify launch Activity: Default Activity not found

For main activity in your manifest you have to add this with category LAUNCHER (First Activity on launch app):

<activity
    android:name=".MainActivity"
    android:label="YourAppName"
    android:theme="@style/AppTheme.NoActionBar" >
      <intent-filter>
            <action android:name="android.intent.action.MAIN" />

            <category android:name="android.intent.category.LAUNCHER" />
      </intent-filter>
</activity>

For other activity you have to change category to DEFAULT:

<activity
    android:name=".OtherActivity"
    android:theme="@style/AppTheme.NoActionBar" >
    <intent-filter>
            <action android:name="package.OtherActivity" />

            <category android:name="android.intent.category.DEFAULT" />
    </intent-filter>
</activity>

Check this Activity and this Start Another Activity

So your code is:

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
package="com.example.mrrobot.mycoolweather" >
<uses-permission android:name="android.permission.INTERNET"/>

<application
    android:allowBackup="true"
    android:icon="@mipmap/ic_launcher"
    android:label="@string/app_name"
    android:supportsRtl="true"
    android:theme="@style/AppTheme" >

    <activity
        android:name=".activity.ChooseAreaActivity"
        android:label="@string/app_name" >
          <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
          </intent-filter>
    </activity>
</application>

</manifest>