You may want to look into possibilities of securing even shorter domain name, i.e. ideally it would be http://time.in/London

Lots of possibilities there: querytime.in, gettime.in, localtime.in, thetime.in. Godaddy actually offers .in domains. If I were OP I'd just register then all, and let the ones die that friends and family don't like.

either go super short or go memorable. I think whatsthetime.in works because its literally what you'd ask.

localized versions? Are there any domains like .in which mean "in" in other languages?

in is a fairly global word. If you play around in Google translate you will see that in is in in German and Dutch.