Chuckles said:

Our neighbor is putting up an ugly addition, and we would like to
screen it with something evergreen ASAP. It doesn't have to be more
than 12-13ft, but it would sure be nice to have it get to a
functional size fast, not in 10 or 20 years.

We also don't have much distance between the houses, so it can't be a
very deep screen, i.e. the plants have to be narrow.

Any suggestions would be very gratefully received.

Privet, grows 7' per year to 15' tall, looks nice

It's evergreen in my zone, you'll have to check to see if it is in yours.
http://www.hybridpoplars.com/privet.htm
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McQualude