We had a great time in Rhodes staying at Nick and Mike's place. It is a lovely apartment, spotlessly clean, large spaces, good views, and very cosily decorated. It's a homely apartment and Mike is right next door to help with anything you might need (but he is never intrusive).
The location is also great - about a 15 minute walk to the Old Town and a bit more than that to the beach. It may be a bit difficult to stay in for someone with mobility issues, as it is on the 4th floor and there's no elevator. (Obviously this is no fault of Nick and Mike's)
I believe Nick and Mike's place is one of the nicest AirBnb's in Rhodes at this price range - you won't regret staying there!