It's not all that obvious, but you can find everything you're looking for in the registry.
Basically:
you need to inspect the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names\SQL
subkey to find the installed instances and their "internal" names
with that internal name, you can inspect the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\(internal name)\Setup
node to find everything you might want to know about that instance
In C# code (and for a 64-bit OS, with 64-bit versions of SQL Server), this would be:
// open the 64-bit view of the registry, if you're using a 64-bit OS
RegistryKey baseKey = RegistryKey.OpenBaseKey(RegistryHive.LocalMachine, RegistryView.Registry64);
// find the installed SQL Server instance names
RegistryKey key = baseKey.OpenSubKey(@"SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names\SQL");
// loop over those instances
foreach (string sqlInstance in key.GetValueNames())
{
Console.WriteLine("SQL Server instance: {0}", sqlInstance);
// find the SQL Server internal name for the instance
string internalName = key.GetValue(sqlInstance).ToString();
Console.WriteLine("\tInternal instance name: {0}", internalName);
// using that internal name - find the "Setup" node in the registry
string instanceSetupNode = string.Format(@"SOFTWARE\Microsoft\Microsoft SQL Server\{0}\Setup", internalName);
RegistryKey setupKey = baseKey.OpenSubKey(instanceSetupNode, false);
if (setupKey != null)
{
// in the "Setup" node, you have several interesting items, like
// * edition and version of that instance
// * base path for the instance itself, and for the data for that instance
string edition = setupKey.GetValue("Edition").ToString();
string pathToInstance = setupKey.GetValue("SQLBinRoot").ToString();
string version = setupKey.GetValue("Version").ToString();
Console.WriteLine("\tEdition : {0}", edition);
Console.WriteLine("\tVersion : {0}", version);
Console.WriteLine("\tPath to instance: {0}", pathToInstance);
}
}