If you want to get the default page of a publishing template based sites (or any sites which are enabled publishing features), then can directly get it from the PublishingWeb.DefaultPage Property. But, there is no a direct property or method to get the default page of a non-publishing based sites, but it is possible in the following way.

   1: using (SPSite oSite = new SPSite("http://sowmyans1"))
   2:  
   3:       {
   4:         using (SPWeb oWeb = oSite.OpenWeb())
   5:         {
   6:             object oFolderObject = oWeb.GetFileOrFolderObject("http://sowmyans1/");
   7:          // below line worked fine for me in SPS 2010, but not in MOSS (non publishing)
   8:          // string strWelcomePage = ((Microsoft.SharePoint.SPFolder)(oFolderObject)).WelcomePage;                    
   9:  
  10:          // below line worked fine for me in both SPS 2010 and MOSS
  11:             SPFileCollection oFiles = ((Microsoft.SharePoint.SPFolder)(oFolderObject)).Files; 
  12:             string strFile = oFiles[0].ServerRelativeUrl; 
  13:         }
  14:   }

For Publishing sites : http://msdn.microsoft.com/en-us/library/microsoft.sharepoint.publishing.publishingweb.defaultpage.aspx