Disclaimer: Those points will vary based on the city and the hotel or booking engine policies, but they are worth trying and seeing what works best for you.

Trip Length

Don't book very short (1 day) or very long (6+ days) often the best price can be found for a few days length.

Compare different booking engines

Try multiple booking engines, I usually use Booking and Expedia , you don't need a comparison website to find out the cheapest offer, just use Google maps and it would normally show the best price.

Test 1 person and 2 person searches

Sometimes hotels can offer a generous discount for the same room if booked by a solo person, interestingly, some hotels offer cheaper rates if booked as a double, its worth trying both options and seeing which option offers a better price.

Break the booking into multiple smaller bookings

Sometimes breaking one long booking into smaller bookings can save you a lot of money, for example if you book 5 nights, it's worth trying to book 2 nights + 3 nights and seeing if the price goes down.