We've booked at Hostal Adriano - which has had rave reviews here - but I've just learnt they have no safe boxes in rooms or at reception.
Does anyone think this could be a problem? Are hostals fairly safe? Unfortunately I'll have my laptop with me as I'm returning from a conference and would like to leave tickets and other valuables....

I would talk personally to the Manager and ask them to keep my valuables, asking for a receipt.

Since you say there are no safe deposit boxes at the reception you might consider taking along something like a Pac-Safe device which could be used to secure your laptop in your room. Wish I could offer other advice.

Thanks for these really good suggestions especially Bootman4U's one, I'll try and buy this here in Australia.
But of cvourse it won't work for locking up my ticket and travellers cheques. Do most people carry all this with you each day or are you fearful of being mugged (like me!)

Having been pickpocketed in one of my favorite cities (Barcelona--yes I am definitely going back) I cannot urge you strongly enough to wear/use a MONEYBELT..either the kind that hang around your neck or fit under your clothes/trousers.
Of course, during an actual mugging with physical assualt the moneybelt might not help...but believe me, I've cruised around some of the worst areas in Madrid and have never been assaulted, pickpocketed, etc. DO NOT carry valuables in your pockets no matter how tightly your Levis might fit!