I live slightly south of this area (Indian River County as opposed to Brevard), but will chime in.
Viera is the "newest" city and would be the closest to a Military Base (Patrick AFB). They have decent shopping and restaurants as well as many newer housing communities (no idea about schools). The "Shoppes at Viera" is right off of I-95 and has a large outdoor shopping/dining district.
Both Palm Bay and Melbourne are older cities.
In the very south end of Palm Bay (Bayside area) they are doing the majority of the new schools and housing communities. They have recently constructed a new shopping area in Palm Bay just off of the Palm Bay Rd I-95 exit. Also the Malabar Rd. I-95 exit seems to be growing as well.
The major shopping in Melbourne is located along the US192 corridore, the far east end of which is the older Downtown area with antique shops and cafes. BTW, by travelling directly west on US192 you will eventually end up in St. Cloud and then Kissimmee. Melbourne has an airport, however it is small as another poster mentioned. Most flights are commuter sized and transfer in ATL. I ocassionally fly out of there on business, when work is covering the flight, but will drive to Orlando for a much better flight selection/pricing if it is personal.
Not sure what work industries you may be in but MIMA (Melbourne Internal Medical Associates) dominates the medical community in the area and aerospace, engineering, and government contracting companies (such as Harris) make up the bulk of the technical job opportunities.
Hope that helps a bit.