Glasgow's about a 4-5 hour journey away, but nowadays very much worth the visit I hear. Have you thought of visiting Warwick? davem's been and he liked it a lot. Also Stratford isn't far from Birmingham, if you could stand the crowds.
Personally, I'd recommend a trip to the Peak District as you've got big houses like Chatsworth (Mr Darcy's house, allegedly
)and Haddon Hall, plenty of walking with stunning views, stone circles, and lots of pubs. You can tell I'm a frustrated tour guide...