If you're looking at getting into Landscapes and timelapses, then stick with your kit lens for a lot of it.
Buy an intervalometer, you should be able to find them for less than 20$ on ebay or amazon (don't buy the 150$ canon brand 'timer remote controller' that does exactly the same thing... it's not worth it) Make sure to buy the one for the t2i/t3i/t4i (or as they are called in other countries, 550d/600d/650d) etc, not the 3 pin one for Canon's other cameras (there are two different ones - so get the right one. it looks like a mini headphone jack). This will allow you to set up your intervals for when the camera is going to take shots. You can look up how to do it all over youtube.
You're going to want one of these not only for timelapses, but also for long-exposure photography, and getting really steady shots on landscape shoots, because you don't even have to touch the camera when shooting. it's awesome. It allows you to use bulb mode the right way.
As for the lens, the kit lens actually is pretty killer for landscapes. the 18mm wide end of the lens is effectively a 28 or 29mm (on a 35mm camera) - so fairly wide angle, gives you a serviceable f3.5 aperture when wide open, but is really pretty good at f5.6 - f8, where you want to shoot if you're doing landscapes anyways. It's not the sharpest or the fastest, and it's going to give SOME distortion, but it's no worse than the wide end on the faster tamron/sigma 17-50mm options. It's absolutely just fine (this is actually why I've kept it... and it compares quite well at 18mm to that of my 17mm tokina prime lens)
If you are looking for a new lens though, start cheap and buy a 50mm f1.8 "plastic fantastic". It's built like a toy, but it's actually extremely sharp, and gives solid low light performance. It has a somewhat cheesy 5 blade aperture diaphram, but who cares, it's got autofocus, it's sharp, it's fast, and it's less than 100$ used (I bought mine for 80$ on keh.com) The only issue with it is that it comes out effectively to an 80mm lens. So it's a bit tight for most photography that you may be doing, and certainly not appropriate for landscapes or anything wide. It's made better for doing basic portrait shots and low-light shots here and there, but it's anything but wide on a t2i. Still absolutely worth it. I had the f1.4 50mm lens, but I got rid of it because it because it was inaccurate and not worth being 4 times as much. You can also throw down some extra dosh, and pick up the 50mm f1.8 mk1 version of the lens, which was the original version built between 87 and 1990, that had a much better focus ring, and a metal rear mount. They will run you about 150 rather than 80-100, but they are the same exact optics in a far nicer package.
If you want to get something a little bit wider, or say, 'standard' (that is, a field of view of a 35-50mm effective focal length on your t2i) you're going to want to go with a wider lens. 24mm, 28mm, 30mm, and 35mm lenses are going to give you this option.
Canon makes 24mm f2.8 (38mm on a film camera) and a 28mm f2.8 (comes out just wider than a 50mm on a film camera), both of which can be had for about 250 used... but neither are really that fast, and for a little more if not the same (about 275-300), you can buy a 35mm f2 that will be a lot better (56mm on a film camera), and faster with maximum aperture of f2.
If you want faster than that, Canon makes a 28mm f1.8, and Sigma makes a 30mm f1.4. I personally have the Sigma, and the used price for it is well under 300$ now (i snagged mine for 215 shipped to my door). It has it's limitations though, and a lot of folks would suggest you spend about 350-450 on the Canon built 28mm f1.8, which can not only be used on film cameras and Full Frame digital cameras (if you decide to upgrade later), but doesn't have the Sigma 30's AF issues that many people complain about, and it's a little sharper here and there.
Honestly though, and perhaps I got a good egg with mine, but for less than 300$ used, the best price-quality option for a Crop Standard for your t2i is a sigma 30mm. I've been very happy with mine, and it is the closest you'll get to a 50mm effective look, and it's f1.4, which is nice even though it's soft as hell at that aperture (like everything else). Something to be noted though, is that it really doesn't work on a 5D, because the image circle is too small. Oh well, sell it if it comes down to that.
I have a bunch of different lenses for my own t2i and 20D, but I usually just use the Sigma 30, the 50 f1.8, and the kit lens. I'll throw in my tokina 17, or my Canon 24mm every once in a while, but eh.. I tend to go with what works.
anyways, this opened up a can, and I really just need to fucking do an "official 'WHAT LENS SHOULD I BUY" thread...