OK maybe it's not close to ALL castles, I mean there are plenty plenty of them.
But the location is pretty good anyway and the city itself is nice.
The Atlantic coast and Brittany (Bretagne) are both about an hour from Angers if you want to see more than just the Loire Valley.
You should be able to reach all castles during a day so just take a whole day off, pack a picknick bag (if it's not too cold in September?), leave early in the morning, and combine maybe 3-4 castles during the day.
I think that's the best way of doing it.

Muscadet de Sevre et Maine is indeed a nice white wine from the region, I bought it there to bring home as a souvenir and it was pretty good.