I used to live and work in Wolverhampton until earlier this year, Cooperoo. Where are you likely to be looking to move to?
It's a nice city, I liked living there. The West is very different to the East.
Shopping fairly standard but the centre is nice and compact to potter round. Beatties the department store is good. Easy to get to Birmingham, Merryhill Centre, Shrewsbury, Telford as alternates. Some nice independent butchers etc in the villages of suburban Wolves.
Bantock Park is the nicest in my view, great playground, cafe, museum, pitch and put, lovely gardens as well as park. There's also West Park (did a lot of driving round that to get baby asleep...) with nice ducks and Tettenhall with a shallow pool that they only fill in the summer and kids play in it.
Very easy to get out of the city to countryside, particularly on the west side. Sample of our days out:
Bridgnorth funicular tram
Ironbridge enguinity
Weston Park grounds (small train)
Telford park (great sandpit and play areas, the best I've ever seen for free)
Long Mynd walks
Football club fairly key to the city's identity but very very rarely any trouble.
I used to work for the museum service and the three museums (Wolverhampton Art Gallery, Bantock House Museum, Bilston Craft Gallery) are all outstanding and very very good for kids. Bilston has special sessions for making with under 5s.