Kayak and Kiwi are good websites. September 23rd is the most affordable day so far to fly in and would allow for a couple days for mishaps.
You have 2 main options: 1) Fly into Edinburgh 2) Fly into London and take the train to Edinburgh. The venue is about 20 miles or a 30 minute car ride from the Edinburgh city center. We've found that arriving into London is cheaper and you would have a better chance at getting a direct, nonstop flight. This would make your air travel shorter, but the train is about a 5 hr ride from London to Edinburgh. There are trains that leave all day from King's Cross Station. (Harry Potter 9 3/4). We recommend buying these train tix in advance to save a significant amount. If you don't want to ride the train, RyanAir offers one way flights from London to Edinburgh for around $47.
If you feel comfortable driving on the opposite side of the road then go for it! Especially if you are planning on extending your trip. Please take note that most rentals are manual unless you specify that you need an automatic and take note that you will be shifting with your left hand. If you don't rent then Uber is an option.
Look up hotels or AirBnB in Midlothian or Gorebridge.
This will be specified on the invitation.
This is a maritime climate but much like fall in the east coast. September is a rainy month in Scotland. Temps range from high 40s-low 60s. Pack accordingly.
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