In an honest world, cash would be the only way to go. Everyone accepts it, if fits in your pocket and you don’t have to remember any pin numbers.
In the real world though, only those with faith in their guardian angel would carry too much of it around at any one time. It’s definitely worthwhile keeping some dollars on you (the universal currency) in case of emergencies and you can keep a couple of different stashes about your person.
A thin money belt that you can hide with no significant bulge behind your trousers is a good bet. Most theft happens while you’re unawares and so if it’s close and tight you’ll feel any prying hands.
The same is true with the front pocket of a pair of jeans. However if you are mugged then it will be found for sure.
The really paranoid sometimes use a dummy wallet or money bag with copious change so that the attacker will feel like he’s made a big score – he’s unlikely to want to hang around and check.
Another possibility is to hide money in your shoes. In many cultures anything to do with the feet is taboo and even thieves have their self-respect.
If you need to hide money in your room while you’re out the bin is a good place but very risky if there’s a chance that someone might throw it out. Or if you forget. Under the mattress will not work but inside a book is a possibility or inside a smelly piece of clothing.
If you’re anywhere outdoors you can bury your money wrapped well in a plastic bag inside a tin. Make sure you bury it deeply and in a remote place that you will not forget. Hopefully no curious badger will unearth it for breakfast.
In some parts of the world, such as South America only dollars will be respected. Euros are gaining a foothold but check before you go as cash that isn’t accepted isn’t worth the paper it’s printed on.