I haven't voted in your poll because IMHO two lenses are better for architecture rather than one.
A wide angle lens between 14mm to 20mm on FX would be good to capture exteriors of buildings. There is something called parallax that happens especially when you point a wide angle lens upwards toward tall buildings. The lines of the buildings converge creating this effect. Wide angle lenses between 14mm to 16mm on FX works well to capture interiors of rooms. Rokinon makes a 14mm for Nikon. I haven't used it myself, but others have. I believe it might be a manual focus lens. I'm mentioning it because it is budget friendly when it comes to wide angle lenses.
If the 70-300mm lens you mentioned is the same as the one I have, then it too would be ideal to capture the small details and to zoom in to the tops of buildings, ornamental decorations (gargoyles come to mind), and for a host of other possibilities.
Someone mentioned a 50mm. While the 50mm f/1.8 AF-D lens by Nikon is budget friendly and is a great lens, it wouldn't be as versatile. When you compare a 50mm prime with the 70mm focal length of the 70-300mm zoom, there isn't a huge difference between 50mm and 70mm when looking through the viewfinder. And that's why I'd suggest the 70-300mm zoom over a 50mm prime. The zoom offers more potential simply because it's a zoom--except when it comes to low light. Please don't get me wrong, I have a 50mm prime, and it has its purpose.
But for what you want, I hope you would consider both a tele-zoom and something on the wide angle end. For DX, then you'd have to figure out the comparable focal lengths. If you stick with FX glass, it can be used on a DX lens. Then the only DX lens you'd need to get would be an ultra-wide such as a 10mm, 11mm, or 12mm DX zoom. I think someone mentioned an 11-16mm although I've never used one myself. Something in that focal length would be good on DX.