How can I use a simple Dropdown list in the search box of GridView::widget, Yii2?

You can also use below code

[
    'attribute'=>'attribute name',
    'filter'=>array("ID1"=>"Name1","ID2"=>"Name2"),
],

OR

[
    'attribute'=>'attribute name',
    'filter'=>ArrayHelper::map(Model::find()->asArray()->all(), 'ID', 'Name'),
],