I have an ASP.NET website written in C#.
On this site I need to automatically show a start page based on the user\'s location.
Can I get name of user\'s city
What you need is called a "geo-IP database". Most of them cost some money (albeit not too expensive), especially fairly precise ones. One of the most widely used is MaxMind's database. They have a fairly good free version of IP-to-city database called GeoLity City - it has lots of restrictions, but if you can cope with that that would be probably your best choice, unless you have some money to spare for a subscription to more accurate product.
And, yeah, they do have a C# API to query geo-IP databases available.