Considering that you do a fair bit of portraits and landscapes, I'd recommend a body with its kit lens (either Nikon's 18-105 or Canon's 18-135, depending on which system you end up with), plus a wide angle lens such as a Tamron 10-24mm for landscapes, plus a 50mm f/1.8 or f/1.4 lens for your portraits.
If you decide on Nikon, for $1800 you could get away with a D7000 plus 18-105 for around $1400, the new 50mm f/1.8 AF-S for another $250 and perhaps an SB-600 flash for your portrait work. If you want a lens a bit higher quality than your 18-105, you could go for the D7000 with Nikon's 16-85mm, but you'd have either no money left in your budget for a portrait lens, or a Nikkor 50mm f/1.8 AF-D at the most. Alternatively, you could try a D90 with the 18-105 for about $1000, a Tamron 10-24 for another $550 (Not the greatest wide angle lens, but it's pretty inexpensive) plus a 50mm f/1.8 G, for a great all around kit.
If you stick to Canon's system, you'd already have a lens for your camera from your 350D (the 18-55 I'm assuming?), so you could save a fair bit of cash buying body only. The 60D, Canon's equivalent of Nikon's D7000 is slightly cheaper and will run you around $1000 brand new, body only. You could add the Tamron 10-24mm to that kit, a Canon 50mm f/1.8 lens for portraits and top it off with a 320 EX flash. Tha t would pretty much get you ready for most situations. If you're looking at upgrading from your 18-55mm, you could add another $300 or so onto the package and drop the flash, or you could add another $700 onto the package and buy the excellent 15-85mm zoom if you want improved optical quality and drop the wide angle and the flash.
Whether you should go Canon or Nikon is more of a personal choice. Feel out both manufacturer's cameras in your hands, and whichever's ergonomics you prefer should be your choice.
If you'd be willing to stretch your budget a bit, I'd recommend replacing the Tamron 10-24mm zoom with the Tokina 11-16mm zoom, which performs much better optically but costs $300 more than the Tamron.
I hope that I helped,
Gear: 7 Nikon Nikkor AI-S and AF-S lenses, SB-700 flash, Nikon D7000, Nikon FM, variety of accessories
"There are no rules for good photographs, there are only good photographs."
- Ansel Adams