DSLR changed my life in terms of photography and I similarly soon found myself wanting a lens with more reach and started researching telephoto lenses. I chose the 55-250mm primarily as it was the cheapest telephoto and was also the lightest as was travelling at the time.
For skyline shots though you want a wide angle lens rather than a telephoto. I took most of these shots with the 18-55mm kit lens I got with my Canon 550D at the 18mm focal length and the panoramas are just several photos stitched together.

Depending whether you have a full frame or crop sensor DSLR, you would want to get a lens that is 24mm or less for landscape/skyline as you can get more into one shots. Have recently shot with the Canon 16-35mm f2.8 lens which is great but very expensive.

Very envious of you living on Staten Island and working in NYC. I spent a week there last year and you can see some of my skyline shots on my America blog here: http://roryinamerica.wordpress.com/category/new-york/

And more of my photography here: http://roryalexanderphotography.com/

If you have any other questions just let me know.

Rory

From what I can gather, there are more expensive lenses, which might be better suited for night photography, but like you, I don’t want to invest a lot of money until I make sure I’m getting good use out of what I already have. I prefer to upgrade gradually.

Marry Christmas!