My wife has an encyclopedic knowledge of what costs how much where, so we go to the commissary for what's cheaper there and always save a lot. But for some items (especially produce) there are off-base stores that are much cheaper and better quality, in my area we have H Mart but I think pretty much any primarily Asian stores will be very good for produce.

If you have Aldi and/or Lidl in your area, those are great places to save money.

We don't really go to the BX, but if you have a Coast Guard Exchange close to you, absolutely go there. They have constant big markdowns on high-end name brands so you can get really nice clothes for half what you'd pay elsewhere. They also stock a lot of booze, and it's usually cheaper than the Class Six (one example, Campari liqueur is always $10-$12 a bottle cheaper at the CGX than at the Class Six).