Hi Dusty,
I come from a big city in India (called Pune) and there is a lot of light pollution where I used to live. I used to own a 5" f/7.2 reflector back then and I could quite easily resolve Albiero. In fact I remember being really excited on looking at the red and blue of the stars! I could resolve them with a 20mm eyepiece and they looked fantastic with a 10mm eyepiece. I recently moved to New Haven, CT, in the US, and this is much less light polluted than my old city. I enjoy much better views from here, and can easily split Albiero! So, unless you are severely light polluted and cannot see any stars when you look up, you should definitely be able to resolve and enjoy Albiero and many other double stars.
I would also like to mention that if you are contemplating buying a telescope for observation purposes, then you should definitely consider buying a dobsonian. These are the best bang for the buck for visual astronomy as almost all of your money goes into the optics of the scope. An 8" dob from any of the big companies will guarantee not only that you will be able to split Albiero, but also be able to observe most of the Messiers! So do consider purchasing a dob!
As always though, there is nothing that can beat a dark sky. You will always get your best views from a really dark new moon night from far outside the city.
Hope this helps!
Varun.