Buying at a local market is probably the best way to spend your shopping money (if you think of it as your voting power in "real life" - where you put your dollars is where you put your votes and if more people do it, it will keep improving!).
It is also the best way to support the resiliency of a local economy, as most of the time you are treating directly with local producers, building trust and closer human relationships with them and with your food sources! Your money spend will probably stay in the same place with them instead of flying away to the countries where the big superstore's capital is located.
Finally, it also implies less of a carbon footprint which is usually derived when buying avocados from Peru at a supermarket in Great Britain, for example. All the environmental externalities associated with that oil-based supply chain are usually badly misrepresented in the final price you are paying. Local means more eco-friendly. So in conclusion, YES PLEASE, BUY LOCAL!