timing of booking hotels

Pretty sure it depends on how full the hotel is projected to be

well, it's europe in september, so I think they won't be entirely full

Far in advance, prepaid, usually gets the best rate. Last minute rarely ever will you find a deal, unless you're deep into the offseason for a particular destination. Still, if you're in a heavily touristed area where hotels close for the season, drastically reduced supply can actually drive up the prices at the hotels remaining open year round.

Book a good refundable rate and keep looking...
if you find one better...well you know..

But hotels get pricier as occupancy increases.

Booked a hotel through Hilton 3-4 months ago. Am a Hilton honers member. Booked hotel Friday through Monday at a rate of 250 per night. I could cancel up to 24hrs out. Looked the week before, i booked the same room for 120 for the three days. I told my buddy the same day and he forgot to book it. When it was all said and done, I paid 428 and he paid just under 900. Same room for half the price. Best thing to do is book and keep looking.