I start with Tripadvisor as it will give you a rough indication if a hotel has given one of the booking sites a better deal. I'd then go to that site to see if the were any hidden taxes and fees not mentioned. I get annoyed when you see a headline rate, but that's the lowest price over your stay and other nights are dearer but that's not clear unless you've dug around.

I always check the hotel's website and you can get some sweet deals. Stayed in Milan, booked direct and paid the same as what I would have done on Booking.com, but got a suite with a balcony. It was really cool as it was in the middle of courtyard on the 2nd floor.

I also go through the cashback websites to see if I can get an even greater discount. I'm normally fine with booking and paying ahead. Saves worrying about exchange rate fluctuations.

Don't use Airbnb type accommodation because I want the hotel experience.