As much as I love Brighton, December is not when it shines best. The OP may want to consider Manchester. There is almost always some show or event going on, the city centre is VERY walkable, and advance train tickets on Virgin from London can often be had for 10GBP ow.
One note of caution - There is not a giant selection of hotels in the city centre of Manchester. Do not arrive without a reservation and assume you'll just find something. Book in advance and you'll be fine.