Will be landing around 4:30 PM for one night before mid-morning flight next day. I booked Westin Palace. Is anyone familiar with this hotel? I chose this hotel because it looked grand, specious and in a good location to walk around Monday night, have a nice dinner and then leave next morning for the airport. The hotel is under renovations and changing to The Palace by the time we get there.

Any recommendations for airport pickup service? I came across Sixt. Any feedback or other recommendation?

Would love to do a night tour of Madrid but am hesitant to pre-book anything in case our flight arrives late.

Yes, the hotel is lovely and in a great location. I know nothing about renovations or name change.

Sixt in a rental car agency; I would not look to them for a ride to your hotel, although they may well offer transfers.

The best way to get to the hotel is to exit the airport terminal and get on the line for taxis. Taxis have a flat rate, including luggage, of about 33 euro to your hotel. That is what I do when I visit Madrid.
The hotel can arrange a pick cup for you but it will be much more pricey and there is no reason for that. But ifi you choose that option, The hotel driver will have your name on a sign when you exit the secure area of the terminal.