Google Provides two ways to achieve this. If you are not satisfied because in countries like India it do not work well, because states and provisions here do not have rectangular or structure boundaries.
1.LatLngBounds (LatLng southwest, LatLng northeast): Where you can give latitude and longitude to form an rectangle.
2. Location (Lat,Lng) & Radius: Where you can give latitude and longitude to form a circle.
But the problem with these approaches they do not provide expected results if you are from countries like India, where states and provisions are not in structured shapes (Rectangular) as in USA.
If you are facing same issue than there is an hack.
With jQuery/Jacascript, you can attach functions which will consistently maintain city name in text input which is bounded with Autocomplete object of Places API.
Here it is:
<script>
$(document).ready(function(){
$("#locality").val(your-city-name) //your-city-name will have city name and some space to seperate it from actual user-input for example: “Bengaluru | ”
});
$("#locality").keydown(function(event) { //locality is text-input box whixh i supplied while creating Autocomplete object
var localeKeyword = “your-city-name”
var localeKeywordLen = localeKeyword.length;
var keyword = $("#locality").val();
var keywordLen = keyword.length;
if(keywordLen == localeKeywordLen) {
var e = event || window.event;
var key = e.keyCode || e.which;
if(key == Number(46) || key == Number(8) || key == Number(37)){
e.preventDefault();
}//Here I am restricting user to delete city name (Restricting use of delete/backspace/left arrow) if length == city-name provided
if(keyword != localeKeyword) {
$("#locality").val(localeKeyword);
}//If input-text does not contain city-name put it there
}
if(!(keyword.includes(localeKeyword))) {
$("#locality").val(localeKeyword);
}//If keyword not includes city name put it there
});