Need Recommendation for Mykonos Hotel

Hello all! My husband and I will be in Mykonos Oct. 9th - 12th after being in Crete/Santorini/Paros. We could spend an extra night in Paros and just 2 nights in Mykonos, but think that we need 3 since we want to visit Delos one day and see several beaches another day. We are trying to decide where to stay in Mykonos and would love suggestions. It will be low season so more quiet in Mykonos. We do not care about the party scene (we are in our 60s - been there done that!). We aren’t big shoppers but will enjoy the town of Mykonos for an afternoon. Since there are so may tourists from cruise ships, we thought we would stay at a beach away from town. We are happy to ride the bus to town or pay a taxi (even though it is expensive). We like Katikies, but are worried Agios Lioness will be closed up for off-season. We also like Ornos beach (Santa Marina maybe?) and Plato’s Gialos but it is a little further away from town and a longer commute for dinner. We would love to be able to walk to dinner in a beach town, but are afraid many restaurants/tavernas will be closed by then. I am wondering if we should consider staying closer to town since the beach towns might be so quiet and partially closed down? Does anyone have any thoughts as to what will still be open in beach towns in October? We wanted to stay somewhere quieter with beautiful views without the party scene, but maybe we need to stay in town to ensure we have a good selection of restaurants for dinner. Just reaching out for opinions! Bill & Coo was recommended as it is close to town, but I understand it really isn’t a walkable/safe road and you will still need shuttle service or taxi to town and it is not on one of the nicer beaches. So much to consider! Looking forward to hearing everyone’s thoughts and suggestions!