While a prime lens would offer some slightly better corner quality than a zoom lens, you might not want to underestimate the value of a wide angle zoom on such a high resolution camera body. It should also be noted that a lot of the high cost of Canon L-series prime lenses is due to their very high speed and accurate AF. You may find more value in investing your money in a zoom lens with ok AF rather than a prime with superb AF.
I use the Canon EF 16-35mm f/2.8 L II lens myself, and it is an amazing lens. Sharpness and clarity are excellent throughout its focal range. There is some softness in the corners at the extremes on a full-frame body, but on a cropped sensor like the 7D, a lot of that is eliminated. The focal range of the EF 16-35mm is effectively 25-56mm on the 7D's sensor, and costs about the same as the 24mm L II prime. Optically, the 24mm is better, however a considerable portion of its cost is due to the very high speed, advanced AF...a feature you mentioned you did not need. From a cost benefit perspective, you would get more out of the 16-35mm.
Alternatively, you could look into the EF-S 10-22mm lens. This would give you true ultra-wide angle on an APS-C body, effectively equivalent to 16-35mm. Optically it is inferior to both the 16-35mm L II and the 24mm L II, however it is a lot cheaper than either. It is a slower lens, but for landscape work, that may not matter. The key factor here would be image quality, and sharpness is a bit lacking with this lens.
With a prime lens, you would be limited, and would have no choice but to crop in post processing to get exactly the framing you want. With a zoom lens, you can frame in the field and maximize the potential of your shots. For the size of prints you use at the resolution you print at, a single shot at 18mp that is properly framed in the field could be used to crop out numerous interesting prints (one of the benefits of having a high megapixel sensor.)