I would recommend against vinyl in the bedroom, consider the carpet or even continuing the hard woods. Hardwoods might be nice if you are sewing in there and need to clean up loose thread and scraps of fabric.

But for the mudroom you could have some fun with vinyl options. Think about a cute checkerboard pattern, maybe traditional black and white or something a little more fun like red. Another product to think about, besides just vinyl tiles are vinyl floor planks. Basically it's strips of vinyl as opposed to square tiles, you can have a lot of fun laying up a pretty herringbone pattern in a space like that. I have used that type of product from a company called Centiva, they have some really great options...

http://www.centiva.com/v2/www/Default.asp

Good Luck!