It can be challenging to decide which part of the city suits you best. An important consideration is ease of access to your job, studies, or daily activities. For example, many UBC students/faculty members choose to live on the Westside since the commute is both short and convenient via direct transit service. If your work is in the downtown core, you might choose to live in one of the downtown neighborhoods in order to avoid the fuss of owning a vehicle; work would be a mere pleasant walk away.
Relocating with children is more complex. You must first of all consider whether you want your children attending Vancouver, Burnaby, or other municipality schools. Metro Vancouver is broken up into school districts by municipality. Each municipality is under a separate school board. Whichever municipality your address falls under is the school district for your children. The good news is that the government of British Columbia has a provision for students wishing to attend a school outside of their catchment (attendance, neighborhood) area, and this is referred to as cross-boundary. Many people feel that Vancouver schools are among the best in the metro area, but it really depends upon your situation and priorities.