Hi, You know that you posted this in the England Forum, and that Edinburgh is in Scotland, right? ;) There is a referendum on Scottish Independence from Great Britain (not England) coming later this year, so I would suggest understanding this relationship before you go.
So, you are arriving in Edinburgh after cross-Atlantic flight at 7 AM. It will be after 8 before you get to city centre. I think that the advice to keep going is a good one. i'm not sure that I would go for a formal tea my first day. You can keep going past late afternoon. I find I start faltering in early evening. I try to stay awake until 9 PM.
I want to get on a real schedule rich away. So, you might want to skip the airline breakfast and have some when you get in. Then, by 10:30 or 11 AM do an activity. My favorite thing to do on the first day is to go to the Castle. The views are marvelous and there a lot to see and explore and it will keep you going. Then, on schedule you can have a relaxing lunch around 1 or 1:30. Then you can go for a walk or take a hop on hop off tour depending on your fitness. I often take that time to go to Waterstones and find some local books to read. That takes me over to New Town. Or, if it's a beautiful day, the Botanic Gardens might be a good place to visit. Stop again around 4 and have a coffee or tea. Have dinner around 6:30. In bed at 9.
That's my schedule. It usually helps me get on top of the jet lag pretty quickly.
Pam