I stayed in two hotels in Positano and can offer some perspective.
Some hotels are actually in town, and as soon as you step out the door, you are where tourists want to be, surrounded by restaurants and shops. Look for an iPad map, and find the part of via Cristofero Colombo that forms a sharp delta, almost a keyhole. The area inside is the town of Positano, Murat is in this group, and is really very central.
Some hotels are up the hill a bit, but you can still walk into town. This includes Le Sirenuse and the other hotel I stayed in, Eden Roc. Eden Roc is about as high up the hill as you would care to go on foot. Sirenuse is practically in town. The hotels in this group may have more amenities and better views, but also more street noise from vehicles.
Other hotels are way up the hill or out of the main town. Thus includes San Pietro and some others. If you pick a hotel in thus group, you will have to take public transport into Positano, which to me would be a big minus.
Palazzo Murat is indeed an old mansion, with charming grounds and antique-furnished guest rooms. Many overlook Positano rooftops or face up the hillside - quintessential Positano. Hence, it would be a good choice for a couple. Some drawbacks are very poor internet (none to speak of in the room), and barebones breakfast. Staff are okay but not warm or proactive.