I've just stripped down a set of carbs and am now putting them all back together, all nice and clean.

But when it comes to screwing the float chamber bowls back onto the underneath of the carbs which way around should the float chambers go?

If you look in the Honda parts and service manuals the Screw-in chamber drain plugs on the float chamber bowls all face towards the inside of the carbs. If you look at pictures in a Haynes Manual they face outside. If you then look at images of NC30 carbs on google, some face inside and others outside!

So does it matter which way round they're fitted back on and if it does which way around is correct?

I always work on the basis of access, there isn't a great deal under there, so I'd face them out, so you "could" get to them if need be.