This is an old thread, but I cannot believe no one answered to use the Brew in a Bag method which means you mash in your boil kettle. No extra vessel needed. You line your boil kettle with a mesh bag and when the mash is complete you remove the bag and all the grain.
This is how I brew every time now, and I don't have to store the mash tun any more.
This is a super old thread but I had to deal with this recently and I was very happy with my results. Living in a walk-up second story apartment in Chicago, space being limited I purchased one of these Ikea BRIMNES wardrobes.
As a 5 gallon + 1 gallon extract brewer, this fit all of my equipment perfectly, gave my carboys a nice quiet place to sit during ...
I started off brewing in a dorm room. If you bottle in 12 oz bottles it is more work, but they'll fit under a bed (or at least the one we had). You can easily fit batches of beer under there. Another good option is the bottom of the closet and stack things on top. For both, I like to keep them in the 24 bottle boxes you purchase new ones from.
A boilover is an even greater disaster in a small space situation. A few glass marbles dropped into the brew pot prevents most boilovers. Don't worry, the marbles can take a lot more heat that your stove can put out.