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.
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
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.