Yes, a city or place may be described as 便利. Both of your examples are valid.
However, your statement sounds peculiar:
I know 便利 means something convenient or handy but can it also be used to describe a place?
I would say:
便利 means something convenient or handy therefore it may be used to describe a characteristic of a place
Examples
- Tokyo is convenient = 東京は便利
Consider the above to be a simplified version of the following:
- Tokyo is a convenient place = 東京は便利な場所
- Tokyo is a place which is convenient = 東京は便利な場所
不便
You may use 不便 for the opposite effect:
- Tokyo is inconvenient = 東京は不便
Consider the above to be a simplified version of the following:
- Tokyo is an inconvenient place = 東京は不便な場所
- Tokyo is a place which is inconvenient = 東京は不便な場所