Okay, I do not normally encourage visits to out-of-town superstores. But Chepstow Garden Centre is worth a passing visit because of its new neighbour, the Newhall Farm Shop. Here you can buy a wide range of quality local meat, cheeses, fruit, vegetables, jams and bread. There is also a long freezer filled with 'scoop-your-own' fruits and berries. Though when I visited in early September, the nearby fields were filled with blackcurrants, elderberries and sloes, so maybe you could bring a bag at this time of year and pick your own for free!
Chepstow Garden Centre is a pleasant enough place with a wide range of plants, also lots of stuff for birds, insects and other wildlife.
Very useful is the large Green Room Cafe which sells excellent value meals - for example full Sunday roast lunch for less than 5 GBP. A very popular place (particularly with the older generation) which also has a children's play area. It is possible to pre-book a table by phone.
This market is held every Sunday at Chepstows racecourse,its very good for bargains and fresh flowers in particular.