Part of my aim is to walk as many UK National trails as possible in the process and visit places I have heard of that seem worth a visit.
You may already be aware of this map of the long distance trails in the UK.
Long Distance Paths Chart - http://www.ldwa.org.uk/shop/list_items.php?category_id=5
If not, really recommend getting a copy as it gives you an instant picture of trail combinations to link up.
After OD, if you end a day in Chepstow, there's a small woods right on the south edge of the town (accessed slightly uphill from memory) where you can discreetly pitch.
If staying a night in Bristol itself, recommend the YHA there, clean, good food, good location.
Found the immediate southern approach to Bristol (your departure) unavoidably road walked as the city was ringed by suburbs, though maybe there's a trail tucked in somewhere that I didn't know about!