My apartment has a cheap box bedframe similar to this:

 

 

It raises the bottom of my mattress to about 12" from the floor. I'd like to add another foot or so; it feels too low at the moment.

 

What is the best way to add height? I am considering a new, taller bed stand, or a mattress base. The bed is a queen size.

Kneel on the floor measure the distance between the floor and your crotch and subtract 6 inches. Perfect height for bed. For me that is 16 inches.

 

But yes 12 inches does seem a bit low for putting on ones socks. The one I currently sleep on is 1/2 metre.

 

If you can find some a layer of pallets under the bed but that would only add about 5 inches.

 

Put a cheap mattress under your current one? 

It can get more height by fitting wooded legs.

If you do not know how to do it or able to find someone to do it for you put another extra firm mattress underneath the existing one. 

It’s actually a really simple job, measure length and width, buy 3 boards that are a little over the length and 3 that are a little over the width (you will probably have to get much longer boards that you cut down) get the wood yard to plane them smooth and rip them to the width you want. They will almost certainly cut them to length as well. 
 

you probably want boards that are around or over 1.5” x  15” before planning and ripping. 

Make, you can just use screws to hold it, or get made a frame that is the exact size of the base, add a cross to the centre (this will depend on the internal bed base structure)

You should add positioning pieces around the top of the frame. Paint it if you like. The whole thing shouldn’t take more than a morning to make them the painting time. 
 

The bed base will just sit on the extra base, you can add some screws for piece of mind if you like. 

Add a box spring? 

people on this forum are trying to solve the problems of the world [and each other] and you are worried about this?

 

ok - finally something that can be solved... hope it works out ok. 

43 minutes ago, bankruatsteve said:

Add a box spring? 

 

Exactly. Or a new mattress. I was in a rental for about five months and the bed was too low and had a SG mattress. Bought  a nice new mattress an threw it on top, or at least the guys that delivered it. Perfect height and great new comfort. Took it with me when I moved.

 

A few house bricks could be your salvation....