"Landscapes and urban spaces".... An ultrawide (UWA) lens would be my first recommendation, too. You don't need f2.8 for that type of photography, either, typically.
If you go this route, virtually all the lenses you'll be considering will be crop only, so don't worry about it, since you use crop cameras now. There is exactly one zoom lens that qualifies as truly wide on your crop camera now and is also FF, so would be usable in 3-4 years if/when you get a FF camera. It's the Sigma 12-24, sells for about double what you want to spend, and has relatively strong WA distortion effects.
Buy a crop only lens now, shoot with it for 3-4 years... then if you do happen to get a FF camera, sell this lens and buy a FF lens then. It would be foolish to limit your gear now, in order to accomodate some camera you might get in 3-4 years.
The Tokina 12-24/4 is a crop only lens, but is partially usable on full frame. You can pick up a used one for well within your budget. Or a new one currently sells for $449 (at B&H). It's a good lens, I'd rank it second only to the Canon 10-22 because it's not quite as good handling flare (the Canon is exceptionally good, the Toki is merely very good). Build quality, I'd rank it ahead of the Canon. It's almost "L-like".
The Sigma 10-20mm would be a decent alternative, a little wider. At the wide end, 2mm does make a difference. This lens is a newer version now, than one I tested a few years ago (when I bought the Tokina instead). Still, I'd rank it third in image quality, but ahead of the Canon in build quality.
There is also the Tamron 10-24mm. It's got the widest range of focal lengths in a single zoom, of any in this category. I found it a little soft at the 24mm setting, but pretty good at other focal lengths.
Both the Sigma and the Tamron copies I tested weren't as good handling flare as the Toki and Canon.
Flare is more likely an issue with a wide angle lens than other lens types, because all too often the lens' wider angle of view includes some bright light source. Also, UWA lenses are much harder to shade very effectively with a lens hood.
There are some other ultrawides, but they are all well over your budget. Besides thre fact that it's more than you wanted to spend, I would not recommend the Tokina 11-16/2.8 to you for three reasons... First is that for the type of photography you say you want to do, you'll normally be stopping down, won't need f2.8. Second, one of the trade-offs to get f2.8 is a very narrow range of focal lengths, only 6mm (a 1.45X zoom... most of the others are at least 2X). Third, another trade-off to get the big aperture is that this zoom is probably the most prone to flare, among all the UWA. If you need f2.8 for some reason, this lens is it and it is sharp... at least equal to the Canon. However, there are several big trade-offs to get f2.8.
I mentioned that the Tokina 12-24 will work on FF. Out of curiosity, I tested it on my 5DII and it works fine as wide as 18 or 19mm, with minimal vignetting. I wouldn't use it any wider (not only is it possible it will vignette, there's also risk of the rear of the lens hitting the mirror in the camera). I have not tested any of the other lenses mentioned, and I don't normally use it on FF anyway... I have an EF 20/2.8 that serves well as my wide lens on the 5DII. Nice to know the Toki can serve as a backup, anyway. It has more WA distortion than the 20mm, though.