A double room is a room occupied by 2 persons. I will either contain 2 twin beds (sperate or pushed together) or an actual large bed (approximately an American double to queen size).

I have to stop scanning headlines. I apologize. I read your title as "Define Double Rooms"...so I defined it...sorry!

I hope someone who's actually stayed there will respond to this posting. I get the impression from their website that some of the basic double rooms have shared balconies while others have private ones. If you send them an email to ask for a private balcony, hopefully you'll get a response. But if not, keep in mind that as long as the room has a view of the caldera you're still getting a great price regardless of the size of the room. Most rooms in the basic hotels are small, it's part of the architectural style. There's not a lot of usable space on the cliffside. You'll understand once you're there.

By the way, here are some directions to the Delfini in case you do end up there:

The easiest way to get to Oia from the airport is by taxi for 20 euro. Or if you're coming by ferry to Santorini you'll be taking the port bus (1.6 euro) into Fira. From Fira you can either take the taxi (10 euro) or the bus (1.1 euro) to Oia from the bus square there. The taxi stand is right next to the bus square along the main road, just uphill and to the right.
Regardless of how you get there you'll know you're coming to Oia by the fact that after leaving Fira, Firostefani and Imerovigli you won't come to another village until you're approaching Oia. The taxi or bus will pull around a curve in the road and you'll be able to see Oia off in the distance, it's quite a lovely sight and you can't mistake it for anything else. This may sound strange, but sit at the right window of the bus or taxi so you can easily see the landmarks I'm going to give you. Oia has it's own small neighboring village/annex, Finikia, which isn't actually separated anymore. They're connected the same way Firostefani is connected to Fira, by expanding development. What I'm saying is that as you begin your approach to the heart of the village you'll first be passing through Finikia. Not to worry. Look for the Anemomilos Hotel on your right, that'll let you know that you're actually past Finikia and are entering Oia. Just after you've entered Oia keep an eye out for a fork in the road. On the right, just before the fork is the Laokasti Villas and Restaurant. Across the street is the Church of St. George. The left fork might be blocked or chained off since it's not really for traffic. In the "V" of the fork is a small hair salon, at least that's what it was last year. The bus or taxi will take the right fork. Be looking ahead of you on the right. Just past Laokasti is an open field, and just ahead past the field you'll see the Musses Studios, set back from the road behind the Filotera Villas. You can't miss the Musses sign on the side of the building. As soon as you see this indicate to the driver that you want to stop. Hopefully that'll be in the road in the area in front of the Filotera Villas and/or the Restaurant Alikona which is right next door. Across from the Restaurant Alikona is a foopath/driveway alongside another building that will take you to uphill to the footpath on the edge of the cliff. You'll see the rental office for the Filotera Villas in front of you as you approach. Turn left and walk the very short distance to the entrance of the Delfini. It's that simple. If for some reason these directions don't work, if you arrive at night and miss the landmarks I've given you, don't worry. You'll end up in the bus square and you can walk back along the road for 5 or 10 minutes to the Restaurant Alikona and just follow the rest of the directions. [One other remote possibility for confusion is if you take a taxi from the airport and the driver chooses to take the secondary road along the far coastline into Oia instead of the regular road. If this unlikely event happens, don't panic, he'll just let you out at the bus square and you can walk back along the road to the Restaurant Alikona.]

Thanks brotherleelove I will be printing out your directions to take with me! And thanks sandi for your "help" - LOL!

I know it seemed silly but people have asked the question about the difference between a single, double and triple. Just trying to do my part!

I did email Delfini - two days ago now - to ask about the baloncy situation with the double rooms. I haven't heard anything back yet . . . I wonder if they are already full . . . I also emailed a number of other places asking about availability and have only heard back from one. Is this typical, or should I jump on the one response I did get?

I'ts typical in that during the off-season it's not unusual for the person on their staff who's fluent enough to respond to an English-language email to be gone for awhile. Maybe they live in Athens like so many other workers in the islands, or maybe they're on vacation somewhere. Hard to know. I doubt very much if they are already full. Try waiting a few more days, or if you can, try a phone call.