If you are playing tourist... skip changing of the guard at Buckingham.
Instead go to the 4pm Household Cav Dismount Parade. Its on Whitehall where the horse mounted soldier sits all day. There are lines on the ground, ask the security/cop where to stand. Basically if you stand with your toes on the line, they will not allow anyone to get in front of you. You will be front row for the show. The show at Buckingham, you are behind the fence line and really don't see much.
https://changing-guard.com/dismount-parade.html