I don't mean just cheap, but a bargain.
If you decide to buy a used sofa bed, replace the matress..never know what could be living in there!! To buy new, you can try IKEA or if on the west coast Jennifer Convertables. Good luck.
It depends which country you live in! If you are looking for a bargain - I'm guessing you don't mind if it's used or nearly-new - it that's true check out the local classifieds. Also remember - wherever you shop - the seller wants to sell MORE than you want to buy - so you can always knock the price down. If its too expensive, you can walk away. The seller still needs to sell it you still have your cash!
Try Sofa Mart. My best friend bought some furniture from the furniture row and really liked it. It all priced fairly well, but isn't built cheaply.
Henco Furniture is a good place. It is in Selmer, Tn. They even have a lay-a-way and 6 months same as cash options. Good Luck and Happy Hunting