I usually look for hotels from Google Maps. There is an option to select the dates there, but they default to some point in time in the future. Right now when I load it, it says Aug 3-4th. I rarely bother changing this, as I just use it to get a ballpark idea of pricing, then go to the hotel website itself to book directly.

Not sure about Google, but more than once I was about to book a flight on Expedia for the wrong week because by default it suggests a date 2 weeks from today, and if I need a flight for this weekend, I often pick the wrong date.