Manchester is a great city, quite a few things to do but much smaller and easier to get around than London. Depends on your interests but I'd recommend a walk round the Northern Quarter and the canals.
You're quite close to the Peak District in Manchester too, I'd recommend that area for getting out of the city. Theres the Blue John caverns, and that's surrounded by quite a few small towns and villages like Chapel-en-le-Frith, Glossop. Also Buxton in that area is very nice too.