Using subquery's alias in a WHERE statement

Try using a derived table instead.

SELECT p.PatientID, p.PatientType, p.AccountNumber, p.FirstName + ' ' + p.LastName PatientFullName, p.CreatedDate, DATEDIFF(hour, p.CreatedDate, GETDATE()) TotalTime, bg.AvgBG 
FROM Patients p 
JOIN (SELECT PatientID, AVG(BGValue) AvgBG   FROM BloodGlucose group by PatientID ) BG
    ON BG.PatientID = p.PatientID 
WHERE AvgBG > 60;