Hi, you wont get a hotel with a pool in the village. The hotels with a pool are mainly in the Krana area which is above the village. There are other hotels with pools, but they are around 2K from the village and are very expensive.
During the day, the village gets packed (overly so) with day trippers, but by mid-late afternoon they have all gone. The evening is the best time where you can enjoy a meal in one of the roof top tavernas and enjoy a drink in one of the many bars.
Have been to Lindos may times, but never actually stayed there, (stayed in Pefkos) but next year we are staying at the Rafael studios which are in Krana. 10 minutes stroll down to the village/beach. Only downside is the walk back up! But you can get a taxi for minimal cost.

We stayed at the lambis studios which have a pool/bar about 5/7 min walk to the main road then 5mins to the village they are set back and quiet

It's been a long time since we were there but I've checked and the apartments we stayed at are still on the go and have good reviews. Look at Krana apartments. Lovely pool. It is at the top of the hill so a bit of a climb at the end of the night but all the Lindos is hilly. You will find you will have sore calves a couple of days in but this soon goes. Just look at it as good exercise! Best not to wear high heels either! It's a fantastic place. Love all the quirky bars and restaurants.