What is a safe way to carry money and passport at night?

The only reasonably safe way to carry valuables is near your skin, under several layer of clothing and in a pouch that does not show through your clothes. Keep that pouch with you 24/7, into the shower cubicle with you. A waterproof pouch that ties around your waist is the best, in my view.

Best have some ready to use money and maybe one card in an outer pocket, in a wallet would be good.
That way you do not need to go into your hidden pouch out in the open, so you do not reveal its existence. And if you are pick-pocketed or even stopped and asked for your money at knife point, rare as that is in Europe, you can give them something while the most of your valuables stay hidden. Any bank or credit card would do for that, one that does not work anymore better than one that does.

But the best way to 'carry' your money is still not have it on you.
If you trust your hostel, you could put most of your money in a sealed envelope and have them put it in their safe for you. But banks are the best, using ATM, as you are likely aware of.

Hostels pretty much always either have safe where you can put valuables, or if not they'll hold valuables for you at the reception desk. It's getting more common for some hostels to have big lockers or cages that will fit your whole backpack.

If I don't want to bother with those options, sometimes I'll sleep with my valuables in a pocket in my shorts. Or maybe in a pocket in my backpack, with my backpack at the foot or head of my bed under the covers.

But really, theft inside hostels is pretty rare. At least 99% of the other people staying in your dorm would be more likely to stop a thief than to steal something. So it's not easy for a thief to steal something with all those people who may be watching. There are occasionally reports of people who suspect that a cleaning person stole something, so you probably shouldn't leave valuables in the room while it's being cleaned during the day (just as you shouldn't at a hotel either).

What I would do is to find a taxi. If it is very expensive I would walk. I would try to find which streets or neighbourhoods are the safest ones. Any way, I would split money around my body, in order to don't have all my money in the same place. Here you have a website where you have 5 tips to keep ypur valuables safe in a hostel; safety in hostels In my experience, I would say hostels are safe. But if you can find hostels with safety box, it will be better.