A Symi/Lindos holiday sounds a nice idea and you should be able to organise that easily.
Allan: by Symi Visitor, do you mean anyone advertising on this site will charge per night?
No, I mean accommodation provided by
Symi Visitor Accommodation http://www.symivisitor.com/Accommodation.htm and I mentioned them because I know about their booking policy. I'm sure other accommodation providers will have the same per-night bookings. There are no big hotel chains on Symi, the hotels, apartments and houses tend to be small family-run businesses and will be very flexible about your booking. Obviously they are used to people arriving at odd times and staying for only a few days so things like check-in and check-out times are not set in stone. Symi is a friendly laid-back kind of place and no one is trying to rip you off.
Also can anyone recommend a hotel very close to Rhodes Ferry Port to stay overnight when we arrive?
Everyone has their own favourite so I'm sure you will get several recommendations here. I usually stay at The Plaza which isn't the closest hotel to the port but it's one I like. The owners are from Symi and it's used a lot by Symi residents if they need to spend time on Rhodes. The all-you-can-eat breakfast is good too
It's a 15 minute walk from the hotel to Kolona where the high-speed catamarans (Dodekanisos Pride and Express) dock. Not too hard if you travel light. Alternatively it's a few minutes in a taxi if you're too full to walk after the huge breakfast.
Panagia Skiadeni, the bigger ferry leaves from Akandia which is a lot further from the centre of town so you'll probably need a taxi regardless of where you stay if you decide to take that boat.