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Hi manduria,
while my calculator says that 4 inches equals 116 millimetres Gary reckons the best "metric" equivalent tire is 110/90-18.
Yes, a 120/90-18 will also fit on the rear rim and not rub on the swingarm etc.
Mind you, the tire size that will work best for you is not necessarily the one that Gary prefers, eh?
It's not gospel but should give you an idea of "modern" tire / rim selection thinking.
stock front rim 1.85/19
stock rear rim 2.15/18
Lots of guys run "too wide for the rim" tires without dieing, IMHO it degrades handling.
A lot of motorcycle handling knowledge has been gained since the rim widths for the XS650 were spec'd in 1969.
In general you want the tire to not get "too tall" for the rim width.
Short and wide is more stable than tall and skinny, eh?
I should add; my bias is for curvy street riding, if your streets are more like trails or you go off road then certainly tall fat tires help cushion shocks, and protect rims from rocks, potholes, curbs, etc..