If it's something that, if lost, would compromise or somehow ruin my trip, then it goes with me. Period. Never used a hotel safe, certainly would not consider hiding valuables in the curtains. I travel solo so if I lose cards or passport I'd be really inconvenienced.
I use a belt loop pouch that goes inside my jeans and that contains excess cash, driver's license, debit card and spare credit card. In my cross-body purse I have my passport, cash for the day and a credit card; my wallet (more of a pouch, really, as I leave my regular wallet at home) has a clip so it's attached to the inside of my purse down at the bottom. This system has worked well for my 5 trips.
I don't know if you're a man or a woman--men have to secure wallets in buttoned pockets or wear in front pocket--or if you're travelling alone, but each person should carry their own bits, in case one is robbed the other has cards, etc.
I was recently in Prague and it can be jam packed with people so you really do have to be a bit more alert in a close throng of people.