Bit of a tough call here. Landscapes generally need wider lenses, and wildlife generally needs telephoto lenses. Portraits could work at either end of the spectrum, really. If you don't want to have to get very, very close to wildlife, a telephoto lens would be ideal.
Single Lens + Extender or Two Lens Options
A lens that might do the job is the Canon EF 70-200mm f/4.0 L IS USM lens. This is one of Canon's more popular lenses, and prices in at about $1300, which is well within your price range. It has a rebate right now that takes it down to about $1200. Combined with a 1.4x Canon Extender, you could extend its focal range to 98-280mm. That would bring cost up to about $1700-$1800. You would be lacking on the wide end, but telephoto landscapes can be stunning and unique (and often more interesting) than their wide-angle counterparts.
If you go the 70-200+1.4x Extender route, you might also want to bring one wide angle prime lens as well. The Canon EF 28mm f/2.8 lens is super cheap at $200-$250, decently sharp at f/4, and super light weight. You would hardly (if even) notice it in combination with the 70-200mm. The Canon EF 50mm f/1.8 is even cheaper and lighter, at $99.
If you don't mind buying an EF-S lens (short-back focus lens that only works on APS-C Canon bodies, not the APS-H or Full-Frame bodies), then there is another option that might do you well. The Canon EF-S 18-200mm f/3.5-5.6 IS lens is a decent lens that prices at $500-$600. It has an 11x zoom range from 18mm to 200mm, but it is not compatible with any extenders (due to the short-back focus), so you wouldn't be able to extend that to 280mm with the 1.4x extender. A 200mm telephoto focal length isn't bad for wildlife photography, but won't really get you in close. Given the super cheap cost of this lens, you might also want to grab the Canon EF 300mm f/4.0 L IS USM prime lens for wildlife work if you think you need it. It costs about $1200, making the total cost of both lenses about $1700-$1800, close to your price range. The 300mm prime is an excellent lens with GREAT optics and quality, ideal for wildlife photography.
Single Lens, Do Everything Options
There are a couple single lenses that will do the job. They cost a fair amount, more than you are looking to spend, at $2400. The two lenses are the Canon "Do-Everything" 28-300mm f/3.5-5.6 lens, and the Sigma "Bigma" 50-500mm f/4.5-6.3 lens. Both of these lenses cover a very long zoom range, and are pretty large and heavy to do so. The Canon covers 10.7x, and the Bigma covers 10x zoom. Both would work for landscape, portrait, and wildlife. The Bigma has better reach, and would be better for wildlife and particularly bird photography. Optically, these two lenses are pretty equal, although I think the Bigma is a little softer. Both lenses offer image stabilization, which offsets their tighter apertures a bit, allowing them to be used hand-held in a lot more situations than they would otherwise be.