Does such a place exist in Manchester? No kids? Not sure if it does! There must be some places near Trafford that have little pockets of estates more suited to older people with grown-up kids. Have you tried Urmston or Flixton? Chorlton has all your pubs & culture but it's more like studentville. Burnage was cheap, I rented an ex-council house there for a while and that particular area was very quiet (although there were families). You could always head down to Cheshire if you can afford it, it's still commutable. Or over south Tameside / Stockport, there are some nice villages further afield but not too far.
When we moved into our area we got some funny attitudes from the older folk (most are retired) because we were in our mid-twenties and they thought we'd be having parties and fights every night. We get on really well with them all now and have a toddler as well. Don't tar every young family with the same brush, they could become your nicest (and quietest) neighbours. We certainly aren't noisy.