I don’t know about others, but some of my friends and I have more than once run into the problem of no ashtrays in non-smoking rooms. Let me explain why: there’s nowhere to throw used napkins, bits of paper and any other rubbish. In decent cafés the waiters do whisk dirty napkins off the table, of course, but I don’t find it all that pleasant. You feel like you’re being watched :)
I suggest solving this problem with special tabletop trash bins. It could be a scaled-down copy of an ordinary trash can, with a lid that opens when you press a little pedal with your finger:
(Image lost: a picture of such a bin, taken from a Kimberly-Clark product page.)
Why go to such lengths? Because if you just put out an ashtray, people will think smoking is allowed after all, plus you can’t fit several napkins in an ashtray: they’ll spill out, which isn’t pretty :)