All sides quarter-sawn!

David Marks did an episode of woodworks several years ago where he built either an ottoman or small mission style table out of qtr sawn white oak. The way he got all four sides to be qtr sawn was to resaw his own veneers and glue them up on the sides that were plain sawn. I think this concept would also work with commercial veneers, as long as they were not paper backed.
http://www.djmarks.com/woodworks.asp here is a link to the list of episodes, they are also on diynetwork.com

-- Joey, Magee, Ms http://woodnwaresms.com

It would look great! You could consider putting quarter sawn veneer on the flat-sawn side.

... oh, Joey and I were posting at the same time. Brilliant idea Joey!

-- Coffee is best with a fine layer of sawdust on top. -- http://www.north40custom.com

The old Stickley furniture used veneers to cover the flat sawn side, but if you look at the antique pieces, nearly all have cracked veneer. I use the 45 degree miter method and you can also use the lock miter joint. I don’t care to do this joint unless I can do it with a shaper. Also it helps to do it in progressive cuts, to prevent tear out.

-- Tim -- http://tmuli.com

Leopold and John George Stickley used a rabetted miter to accomplish this same trick with solid wood. It takes a bit more time to mill up, but it’s easier to glue up. You end up with a leg cross section that looks like this:

-- Daniel, Southern Indiana -- "Have nothing in your home that you do not know to be useful or believe to be beautiful." -- http://blackdogwoodshop.etsy.com

Veneer or mitered joint.

-- Gary, East TX -- The longest journey begins with a single step.

I have done lots of 4 sided quarter sawn square parts. If you have a good saw & can rip consistent 45’s that is definatly the easiest & you will use the lest amount of wood. If your 45’s are a little off. or you ocasionaly burn an edge or two plan on ripping slightly oversize parts and clean them up with a 45 deg bit in a router table.
I only use the 45 deg lock miter bit on legs thicker than 2” (such as a bed with 4” sq. legs”) It uses up quite a bit more lumber but makes a very strong leg.

-- http://www.grandprairiewoodworks.com

Ditto on above; use veneers or miters. Veneers can be tricky if your leg blank or veneers aren’t perfectly flat (i.e. snipe, too much sanding in one spot, etc…), and might have gaps if you don’t get good, even pressure across the entire face. Lock miters are nice if done well (well jointed, straight blank with featherboards, etc.. attached to router table). They produce a consistent joint and it inherently aids in glue-up.

-- Jarrod, Eagle Nest, NM http://anthologyfinefurniture.wordpress.com