Elfina,
We moved from Birmingham after 10 years to the country, not far from the coast.
I loved Birmingham with a passion (not from there originally btw) - we lived not far from Moseley and the general vibe was brilliant. There's LOTS for children - botanical gardens. Kids City at Millenium Point, good pools outside the city, Zoo in Dudley, Safari Park, The Aquarium.
For you - nightlife, restaurants, shopping are outstanding.
Some of the schools are amazing but some are terrible. The real issue is the secondary schools as its largely governed by the 11+ grammar system - and only the top ten percent of those passing that get into the five grammar schools in the city. It depends on how much you care about education.
My DP had a job opportunity that as a family, we couldn't refuse really else we probably would have stayed there.
I have to say though - much as I miss the place it would be hard to move back. It just boils down to much more crime, and my children being more likely to be mugged etc.
It's down to you as a family and what you want?