I live in Oregon and it takes me around 24 hours to reach Santorini without stopping over anywhere on the way. Sometimes I fly out of Seattle and sometimes out of Portland. These flights go to Amsterdam, Switzerland or some other EU airport, but I've never stopped over in London. It's way too expensive for my budget and because of scheduling you have to spend the night to catch an EasyJet flight, which means spending more money on food and lodging. There are none that happen same-day that I'm aware of. I prefer to tough it out and wake up my first morning on the island. It's a serious grind, but I'd much rather recover from jet lag there than anywhere else I know. So it really depends on you and your style of travel, your budget and if you want to visit another country for a day or two on your way to Greece. If you decide to go through London with Easyjet you need to buy your EJ ticket as soon as you can because they don't go down in price, they go up. This means committing to travel dates. If you're not ready to do that you're better off doing what I do instead. If you search for flights from Athens to Santorini you should know that Aegean Airlines and Olympic Air have merged so the schedules are the same on either company's website.
As for where else to go, your closest options to Santorini are Ios, Naxos and Paros and they're all easily reached in short order from Santorini on a daily basis. I prefer Paros because I can also get to Antiparos very quickly by local shuttle boat. I like to rent a motor scooter and putt around the island. There's very little traffic and the scooters have automatic transmissions so they're easy to drive.