big issue in converting string to datetime using linq-to-entities

I don’t think EF supports a translation for a String to DateTime or vice-versa conversion.

As I see it, you have two options, depending on the format of the date in the string field:

If the format is fairly simple, a string comparison might be enough:

// Convert the boundaries to strings first
// TODO: Set the ToString format option to match the database format
string startDateAsString = startdate.ToString("yyyyMMdd");
string endDateAsString = enddate.ToString("yyyyMMdd");

// Query based on string comparison
var memberl = from v in abc.visits
              join m in abc.members on v.member_Id equals m.member_Id
              where v.visit_Date.CompareTo(startDateAsString) >= 0 && 
                    v.visit_Date.CompareTo(endDateAsString) <= 0
              group m by new { m.member_Firstname, 
                               m.member_Lastname, m.member_Id } into g
              orderby g.Count()
              select new
              {
                  numVisits = g.Count(),
                  firstname = g.Key.member_Firstname,
                  lastname = g.Key.member_Lastname
              };

If the string representation of the date is more complex, and a simple string comparison cannot help, you might consider creating a view on the visits table, which does the conversion for you at database level:

CREATE VIEW VisitsWithDate (MemberId, VisitDate)
AS
SELECT MemberId, Convert(datetime, VisitDate, 112) -- For instance
FROM Visits

Followed by importing this view into your DataModel. You might need to do some magic to make the relationships work.

Hope it helps.