I'm managing Liverpool and to be honest, Anfield looks terrible on match days and was wondering if I could maybe change it for say Wembley. So instead of the crappy look of Anfield on match days I would get Wembley instead. Is this at all possible?
Without editing the club details directly no. Your board might expand or might build you a new one at some point, depending on the club you are and the associated stuff.
As for changing your stadium for another in game without using the editor if works are being done on your ground you'll occasionally ground share or be a tenant with another club, alternatively using a national stadium or other such venue.
As Wembley is such a long ass drive away from Liverpool though you'd have more chance sharing Old Trafford than Wembley without editing the data directly!