Having managed hotels for Hilton I can honestly tell you it varies depending on a number of factors including the room type (Kings, Doubles, Suites), day of the week, how booked the hotel is, as well as events that may or may not be going on. Hotels with good management will know in advance when all the big events are so they have the higher rates set over a year out, so it doesn't matter how early you try to book. Some hotels are better at keeping up with events than others. If you find a hotel that seems to be behind the curve with changing their rate levels in relation to events, look them up right away when you want to attend and the earlier the better. I know of some hotels (in other cities, not Vegas) who only update their rates a few weeks or so before a big event. The people who booked earlier, whether they are attending that event or not, get good deals.
Unless you are friendly with a desk clerk that can let you know how a certain hotel manages its rates and when the lower rates are, the online calendars are pretty good at being able to scan for lower prices. Most hotels have something like a "flexible dates" checkbox on their websites (I know Hilton and Marriott do) so you can find the lower rates if you have flexibility in your travel.
If you have already booked your flights and are pinned down to a certain date, then your options are reduced.
