Austin, Here are my thoughts. I lived in Round Rock for 13 years and currently own investment property in Killeen.
Georgetown:
Pros: You are in the path of progress from Austin. Better opportunity for appreciation, close to high paying jobs, more diverse employers, better schools, lower crime, and better amenities. Austin is coming off a housing boom, might be able to time the dip.
Cons: Higher cost. Longer commute to Ft Hood but you are going light traffic direction since most folks are commuting the other direction.
Killeen:
Pros: Lower cost, easier commute to Ft Hood, greater inventory of investment properties, and good deals if you can find them.
If you are open to house hacking you could by a 4-plex for $400k that will generate $3200/month. Live in one side while you are stationed at Ft Hood. In four years when you tour is over you can either sell it for $500-550k, or do a cash out refinance and use your VA loan to buy a place in Georgetown keeping the 4-plex as an investment.
Cons: High crime, poor schools, lower rents, one company town (Ft Hood), property taxes are going up faster than other Texas markets. You really need to pay attention to neighborhoods, a block or two makes a big difference. We have friends who live in Killeen that had a fatal shooting next door. Stay out of old town, Harker Heights or South Killeen are better. I don't believe any of our current tenants are military or ex-military. Low rents primary draw with some commuting into Austin Metro. We own property throughout central Texas and Killeen is the lowest $/sqrft despite being the newest/nicest property. Prices shot up in the last couple years, lots of out of state money. Price/Rent ratio is upside down right now with rents not keeping pace. A year ago we were shopping for more property, placed multiple bids but didn't get anything. Prices were negative cashflow.
Temple/Salado might be a better compromise for a private residence.