You are spot on regarding the areas - the buildings in downtown just off base (76541) are going to be very tough, D class at best. I wouldn't recommend them unless you are experienced and have in-house management on the ground. Most multi-families in 76543 will be the same, with some exceptions (the area just of MLK Jr. Blvd near 190).
There is a LOT of commercial development near the new Wal Mart and newer (yet to be finished) HEB on Stan Schlueter. I own my own fourplex on Alan Kent in that area, and have done quite a few deals with buyers there in the past couple years. I would definitely recommend that area, though at the moment the active fourplexes are usually overpriced (I would aim for 3/2/2/3s in close to $200,000 and 2/2/2/2 for under $190k). There is one on Abigail at the moment that is the most realistically priced, though has very strange floor plan. I'm not sure exactly how you'd classify the area, but at least a C+ if not B.
As for other areas, anywhere in Harker Heights is interesting, though you don't want to overspend there just because it's Harker Heights. Also there are some newer fourplexes and duplexes in Copperas Cove on the north side (out of down town) that I think are well priced for the rents and worth looking into.
Almost all of the newer buildings on the south side (76542 and 76549) are going to be separately metered so that the tenants are paying utilities. Some older builders may have utilities on the landlord. I've never had much experience with paying the tenants' utilities on a multi-family, but I assume the bill can be $100-$200 electric+water, especially in the hot summer months.