You have to add this with the category LAUNCHER for the  main activity in your manifest:
<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>
Just change the category to DEFAULT for other activity:
<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>
your code should be like this:
<?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>
I hope this helps you.