I've done both central London and Surrey... and am from Bristol originally!
I lived in Pimlico for nearly 4 years and as a runner I loved it. Walking or running to work (Westminster is quiet in the mornings and Pim is quiet all of the time), Battersea, Hyde and Green parks on your doorstep, Regents Canal, Hamstead and a shed load of other places like wimbledon a bus ride away. Awesome but pricey.
Now I live in Surrey and its much quieter but the pavements are shocking and routes are less run friendly in general, more running along roads than huge parks to take in. I do like having various canals, london loop, The Thames, Richmond, Bushy and Windsor parks on my doorstep though too.
Wherever you choose you will be surprised about how much is close by if you look for it, check out capital ring and London Loop for some ideas about the variety of terrain you can find in London. Dont forget to join a local club too... if you end up SW way you'll be spoilt for choice!