We would recommend flying into any of the London airports, London Heathrow is the largest and therefore more likely to have a flight to/from your nearest airport. Heathrow also has many transport links to get you around the city or England.
The UK has a great railway system and most cities and towns you want to go to will be easy to get to via train. If you want to see more of the countryside then renting a car may be the best option, but look into the train lines because the UK is a well connected county.
The Things to Do page on our website has some ideas for you but if you need any more suggestions, just drop us a message. We are more than happy to give recommendations!