Roppongi is not "near" Yokohama but, depending on exactly where in Yokohama, you could probably commute in less than an hour each way. That's not bad, when you consider the average salaryman's commute.

The reason you don't see many Yokohama ads in English is probably market related. Realtors probably don't translate the ads unless there's significant money involved and, if there is significant money involved, it's almost certainly going to be spent in Tokyo.

Not that there are not expats in other areas. It's simply a quantity thing.

How much did they allow? If you got at least $2k/month, you'll be fine in Yokohama. Even $1k/month is possible if you don't mind the same size space as many single Japanese.