I moved from Surrey (Kingston, Surbiton, Addlestone split over 10 yrs) to Chichester 7 years ago and I love it. We traded a flat in Surrey for a house with garden and have had both children since moving. We live in a village on the outskirts of the city which has a good cycle link, bus route, walkable etc.
In my experience facilities are excellent here, very good hospital, doctors who I don't wait long for appts, the primary schools are mainly excellent and small with good community feel. I was especially impressed with my care when pregnant with both children. Was very lucky to have the same community midwife throughout for both and hospital care excellent.
I admit that secondary education is the weak area but it is changing and improving and has done a lot in the short time I have been here. A free school has recently started so will be interesting to see how that develops in the next few years. The 16+ further education college has just been graded it's second 'outstanding' in a row.
The town is beautiful and loads of open spaces for the kiddies.
I have never felt like an outsider and found employment relatively easily (administrative roles).
The local leisure centre is excellent and a real family hub.
I have found people friendly and the pace of life less stressful than when living and working in Surrey. I love the fact we know our neighbours and can call on them for help, which we didn't have, despite trying, when living in various properties in Surrey.
The transport links are good (unless you want a fast commuter train to London!) and the opening of the Hindhead tunnel on the A3 has vastly improved the drive time back up to see friends in Surrey, and DH's commute.
Some parts of the city can get crowded in summer, but is comparable to when I tried to get in and around Kingston for the whole of December to shop! And various events at Hampton Court etc etc.
I don't worry about what my children will want as teenagers as their lives could take them anywhere. I lived near London and wanted to get away as a teenager (but am a bit weird like that!) so they might take after me and be happy staying around Chi. And if not we will do our best to support them wherever they want to go.
The move has really worked for us and I am so much happier since moving.
Happy to answer any questions if you want to PM 
Oh, also, imo crime is really not an issue compared with areas I lived. I witnessed the aftermath of a stabbing where I used to live and wouldn't walk late at night on my own, but down here I regularly forget to lock my car since developing my baby brain . I feel very safe.
Sorry this was a bit long..!