Advice for a 2.4 Ghz antenna placement
A first and very important question: What do you want to get out of your antenna? Do you need a wide band or a narrow band? Does it need high immunity to surroundings (such as in a phone, which has to work regardless of how someone is holding it, or when it is bunched up against a face)? Do you need/want a directional channel, or do you need/want more omnidirectional behavior?

A horn could work, provided you had the room for one (at 2.4 GHz they are going to be tens of centimeters in size). Also, a horn is directional - if you want your device to work regardless of the direction, you will need to look at an external antenna. 

If you had actual antenna engineers in your team you could look at fancier designs like slot antennas and leaky wave antennas, but that is not something you can design in a week, even if you are an expert no this. 

Given the constraints, I would look at an external monopole/dipole, as seen in Wi-Fi routers. You can buy these off the shelf and they just "work". If you really want to design something, a patch antenna or other conformal antenna could be done on the outside of the box, but this is a lot harder. Keep in mind that the surroundings are vital - if you design your antenna to work in air, and somebody then puts a piece of plastic on top of it, your antenna will no longer work.