How can I approximate user location through their IP address on server side?

I know there are APIs for doing so but I want to do so as cheaply and locally as possible(without compromising on on quality of guesses ).

For a local solution, you can use a database file. You can find free ones with virtually limited accuracy below:

• Maxmind: https://dev.maxmind.com/geoip/geoip2/geolite2/
• Ip2location: https://lite.ip2location.com/database/ip-country-region-city-latitude-longitude-zipcode-timezone

There exists paying variants with better accuracy. However, when using a local database file, you should ask yourself some questions:

• Do you want to implement the local database file loading/lookup by yourself?
• Do you know how to update your database file with no service interruption (IP allocations change frequently)?
• Is your solution scaling to your needs (in terms of requests/second and latency)?
• Don't you need to deduce transient information (timezone, currency, etc.)?

If the answer is No to one of the previous questions, you should most probably use an IP Geolocation API. I suggest having a look at my service, Ipregistry: it is fast, reliable and inexpensive.