Get yourselves over here!
Anyone coming from the North East I would opt for Continental through Newark. Leave there at 650pm and arrive in EDI at 7am. On the tee in East Lothian by 9am. (40 minute drive from airport) The biggest plus is not going through London and hence playing 'golf club arrival roulette'. The prices have always seemed reasonable and perhaps not the very cheapest but certainly the most convenient.
My advise having seen thousands of visitors over the years is to pick an area and rent a house for the week (even up market holiday lets in Gullane or North Berwick ~ £350 a week) Between 4 guys thats really cheap and you have a base you can work from.
In the summer NB, Muirfield and Gullane No.1 are value for money, with Muirfield being pricey but worth it. There are deals to be had though! Dunbar is a good track bar the views of the cement works at the bottom end, Kilspindie has for my money one of the best short par 4s on the planet with their 4th hole, and The Glen has some of the best views. Luffness is also lots of fun. Gullane does good deals on multiple rounds over a combination of the courses. East Lothian has loads of great, diverse courses, all within 20 minutes drive of a central point.
The same can be said for the West coast, The Highlands and Fife. Come spend your money and help us get out of this mess!