The second parameter of whereIn should be an array of a closure. You are passing a query builder object. If you add ->get() it should work. That is not what you want. It would get that array, and you would make another query to the database. Use a closure

->whereIn('columnName', function($query){
$query->select('...')->from('...')->where('...');
})

In your case

$streetType = DB::table('streetTypes')
            ->select('streetType', 'id')
            ->whereIn('id', function($query){
                $query->select('streetsTypeId')
                ->from('streets')
                ->groupBy('streetsTypeId')
                ->where('suburbsId', 1))
            ->get();

Memory is cheap, execution time is expensive.
Put the street name in the streets table. Your queries become more compex, that slows you down. You have more indexes in you database, that takes memory. I don't think street names repeat frequently enought to make it pay off.