Hi,
Stayed at Atrium Palace in the Villas with private pools last May (for our wedding).
In terms of travel, it will take not very long in a taxi (unfortunately I'm not very sure of the cost), less than an hour I'd think.
In terms of the hotel, I'm assuming you may have elected to go for one of the standard rooms, so I can't really comment on them.
The hotel has nice eating facilities and in the end we had our reception at the Asterias situated near the beach. The restaurant is georgeous and especially at night and found the food very nice. This won't be included in your H/B I'm pretty sure. So it is on the expensive side, although I'm sure it would be worth it for a nice little night there.
The hotel was rather quiet when we where there and was mostly by the sounds of it populated by German/Dutch.
Lindos is only a short taxi ride away, think around 4-6 Euros if memory serves me right.
I'd go back to it in a flash, didn't get the full use of our pool due to going to see friends and family during our stay and organising the wedding. Would like to do it again in a more quieter holiday.
Any other questions, don't hesitate to ask.
FD