I have a very old (1992?) Eagle Creek neck wallet - it's black nylon, not the nude thin neck wallets - and it always goes with me. I don't always use it during sightseeing, but that's what stays on my body in airports & flights -smaller than a purse (though I do like crossbody purses for travel as well) I don't worry about hiding it under clothing, and the strap is actually long enough I can wear it cross body and not just around my neck.

I like the idea of adding a larger pocket to a woman's blazer - depending on your shape, probably easier (and therefore cheaper) to alter than making a man's blazer look right.....