Distances between towns in the UK are relatively close. Unlike the US, domestic flights are not really a bit thing unless you are travelling from one end to another (say London to Scotland). NCL is not really a major airport that would connect to many other UK airports.

You might find hiring a car maybe more convinient in more remote locations. You might have a few difficulities driving on the other side of the road. You might want to consider paying more for an automatic car as well. Most rental cars in the UK is manual (stick) and even if you can drive with a manual gear, changing gears with your left hand instead of right does take a bit of getting used to. Still it is all part of the adventure.

Americans usually are horrified at the cost of things/travels (trains/taxis) in the UK especially with the current exchange rates.

You might consider giving your grandparents a call to get them to phone for a "mini-cab" or "private taxi" to meet you at the airport/train station. It might be cheaper than a black cab you will at the taxi rank, especially for longer distances. That way you will not have to worry about if there will be any taxi available.