In reply to Climbyclaudie:
Depends a bit on which side of Manchester. You can be in Snowdonia or the Lake District within 1.5-2 hours drive of Manchester so it's easily done in a day.
All the closer hills are going to be open heather moorland or grassy hills rather than a rocky mountain but some still give a 'wild' feeling.
To the West, Moel Famau as suggested above.
To the East various places in the 'Dark Peak' including Kinder Low or Bleaklow above Glossop - lots of beautiful hill walking and views and even some short sections of scrambling but not really anything that feels like a true 'mountain peak'.
To the North, Pendle Hill, North of Burnley.
(There are no mountains South of Manchester......
)
Post edited at 21:21