Welcome to DFW!
For groceries, we have found that getting the Safeway app and using Tom Thumb is the best bang for your buck. We also have several Aldi's in the area which are also cheap, but they don't meet SO's quality standards. There are some Asian grocers in my neck of the woods (Richardson), but we don't utilize them really. Sprouts is also nice if you have one in the area. Wednesday is the best day to go, as they have their their sale items run from Weds-Weds, so you have twice as many items on sale.
We both work in education, so we are able to create get all of our clothing choices done at Target and Old Navy on the cheap, so I can't really help with the clothing side.
I don't have a good answer on the activities side, sadly. Ft. Worth can be fun for some days trips. The FW zoo is pretty impressive. The Perot museum is also nice, but not necessarily cheap. Clyde Warren Park is nice to walk around later in the year (when it stops be 105 degrees every day). During the summer, the wife and I tend to have friend over or go to others houses to hang out, go to movies during off peak times (or for free, thanks Alamo Drafthouse and your love of teachers), etc. It's just too hot to be outside much this time of year, imo. The Half-price Books on Northwest Highway is impressive and I could spend the day there personally (also has a little cafe attached).
It can be hard to stick to mustachianism down here since most DFW residents take pride in flaunting their wealth (it is a cultural tradition), but with the low COL and a good job, you can certainly build quite a stache.