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Your question above is an age old question that unfortunately doesn't have any firm answer, but i'll give my thoughts and the process that i use...
Research Rates for the Area - as soon as you are even thinking about a trip, begin to look at rates. Check for your specific travel dates, dates before, dates after, midweek, weekend, etc. This often gives you a very good understanding of what the low end of the range should be, as well as what is considered to be 'expensive'.
Be Realistic - Consider seasonality factors and any special events taking place. For example, if you're traveling to Las Vegas during the Consumer Electronics Show (the largest convention of the year) don't expect to find anything near the low-end of the range you found above.... same goes for locations with baseball Spring Training, College Football Saturdays / NFL Sundays home games, etc, etc.
Book a Refundable Rate - no matter how far in advance your stay is book something that is fully refundable: it can't hurt... and it could help! You never know if your search today is going to be the cheapest you see things, as well, this gives you a firm baseline of what is that you're trying to beat. This refundable rate must be a property that you're willing to stay at for the price; a backup reservation for a 5 star hotel for $400/nite is not good if you're not willing to spend that much for a hotel... nor is the 1 star hotel for $40 if you're not willing to stay at a 1 star property. As most sites show the least expensive rate (which is typically NON-refundable) and it requires a few clicks to drill down to the refundable rate you're looking for, we have created RefundableRates.com which makes it easy to find your best deal on a refundable basis. And a reminder that we almost always have a 5% off Priceline Coupon that can be applied to refundable rates (pre-paid does not mean non-refundable... it just has to be a hotel that you pay Priceline at the time of booking, not a 'pay at hotel' booking)
Monitor / Check Rates Often - if your trip is 6+ months away check rates 1-3 times per week (both refundable to 'better' your reservation from above as well as non-refundable to see if something has appeared that is worth committing to). As your trip gets closer begin to check more frequently. If/when a great deal appears BOOK IT! The best deals often don't last very long so always be ready to act (assuming your plans are firm)... 'marginal deals' you may have a few hours/days to think about it, but if you see a truly great deal don't second guess yourself and act upon it. Don't miss out on $50 savings because you're hoping it drops another $5.
DON'T Recommend Waiting Until the Last Minute - I have never been a fan of waiting until the very last minute to book (and for this discussion i'll define 'last minute' as 1-2 days before arrival). While a hotel guest is typically focused on one hotel stay for one specific set of dates, the hotel revenue manager is focusing on rates for the entire year, and generally speaking there is not much a hotel can do to effect last-minute hotel demand. Take a hotel that typically sells for $200/nite and the day before arrival they lower their rate to $100/nite,.. usually there are not that many people who can suddenly pick-up and go on one days notice in order to take advantage of this new lower rate. As well, by doing so the hotel has cut their rates in half for walk-in customers who show up at the hotel without a reservation (and it's easy to charge these customers the highest prices since most will not sit in the lobby trying to research other hotels in the area for a better rate... they're typically tired from driving and just want to check-in and get to their room). It's also better for hotels to have advance reservations as it's easier for them to manage prices and inventory, they don't want to 'reward' (and train) guests to wait for the last minute.
While the above may seem like a lot of time/effort, it's really not if you use tools to make it easier. We have added a RefundableRates tab to our BiddingHelper.com site which allows you to accomplish all of the above tasks with just one search... just flip between the various tabs to see and compare retail, opaque, and refundable rates.
Some additional timely comments given the current environment:
The covid pandemic has created unprecedented times... especially for travel. I expect hotel rates to continue to be more volatile than usual based upon covid outbreaks and changes in local regulations (lock downs, mask policies, use of vaccination passports, etc, etc). As of this writing the delta variant is on the upswing for the last month or so and (from the areas i have been following) i have already seen hotel rates drop for the months ahead; i would expect to see this reverse (and rates raise) once we begin to see new cases trend downward. There is a LOT of pent-up demand and rates may spike quickly once the general population feels that we are 'out of the woods'.
Lastly, many hotels are operating at limited capacity. Some have blocked off entire floors of their property, while others have required 24-48 hours between guests, etc. so from a pricing perspective you have to consider these rooms 'sold' and effecting demand to the upside. As a simple example, a 4 story hotel that has 100 hotel rooms but has blocked the entire 4th floor of the property... this hotel is considered 25% occupied before selling even one hotel room. From a more macro perspective, if the entire area has 1000 hotel rooms and 25% of the hotels go offline, there are now only 750 hotel rooms available in the area. Hotelier looking at supply/demand view this as lower supply which often equates to higher prices.