The normal advice would be to stay outside inner-city Liverpool. Personally, I'd stay about 100 miles outside inner-city Liverpool.
In truth, there are some nice suburbs, and the commercial centre of Liverpool is not too bad. I'd still start my search for somewhere to live elsewhere.
If you wish to live in Northern England, I'd look across the Pennines to Leeds. A fortune has been spent there over the past 25 years making it a jolly nice place to live.