One end's in zone 3, the other's in zone 2. UNACCEPTABLE! Both ends should be extended outwards.
The southward extension should proceed from Brixton to Croydon, via Norbury. There's no particular reason to go via Norbury, it just happens to be in the right place.
There are three possible ways to get from Brixton to Norbury. Firstly, there's the route along the existing railway, via Herne Hill, Tulse Hill, Streatham and Streatham Common. Secondly, there's the route suggested by Benjamin Nunn, which goes via Streatham Hill and Streatham (and i'd add a new station at Rush Common, TQ306740). Thirdly, there's an easterly route which follows a slightly different railway alignment, to Tulse Hill, Herne Hill and West Norwood, cutting across to Norbury after that (via a possible new station at Upper Norwood, TQ318710). The railway route is extremely wiggly; if it could be built as surface lines, it might make sense, but if tunnelling is going to be done, then it doesn't. Of the other two plans, the Nunn route is perhaps slightly more direct, but the easterly route has better interchange with existing surface lines. All in all, i prefer the easterly route.
Actually, no, changed my mind - stuff interchange, there's a rail desert that needs serving! Basically, south Brixton, the area bounded by Brixton, Streatham Hill, Clapham South and Tulse Hill (with the Brixton Hill / South Circular junction in the middle); it's densely populated and underserved, and generates, i would SWAG, a lot of traffic at Brixton via a bus leg. The new station could be at Rush Common (really the junction of New Park Road and Brixton Hill) or further south, at the South Circular junction (i'd call that one Brixton Hill). There could even be two: Brixton Hill, at the junction, and Brixton Windmill (yes really!) halfway between there and Brixton (also on Brixton Hill, confusingly).
Beyond Norbury, it's more tunnel, under the London Road, via a new station at Thornton Heath Pond (TQ313677), to West Croydon, then on to East Croydon, which would be an acceptable place to terminate.
Assuming the easterly route to Norbury is taken, that makes the southern end of the line: Brixton, Tulse Hill, Herne Hill, West Norwood, Upper Norwood, Norbury, Thornton Heath Pond, West Croydon, East Croydon.
The eastward extension should head more or less east. Between the Chingford branch of the West Anglia and the Epping branch of the Central, the east bank of the Lea is pretty well served, so heading northeast isn't useful; conversely, wandering too far south would make the line a poor competitor to the Central (Hainault branch) and Great Eastern lines. It seems to me that the best option is therefore to head east, crossing the Central line at right angles. The precise route i would suggest would be Woodford, a possible new station at Woodford Bridge (TQ425918), Hainault, a new station in Collier Row (TQ499911), Romford, Emerson Park, Upminster. From Romford to Upminster, the route would use what is currently NR track. If the green belt were to be loosened a bit out here, Whalebone Lane (TQ481914) would be well placed for a huge, soulless housing estate.
This route doesn't make a colossal amount of sense, though; it'd be just as good for Woodford or Hainault as the Central Line (unless you want to go to the City, or Docklands - keep quiet if you do), and the Woodford Bridge station would be useful, but Collier Row, Romford and Emerson Park are better served by the Great Eastern (including a bus hop for the former), and Upminster is better served by the District. It could head northeast from Collier Row, but that's just farms, really, and you can't take livestock on the tube.
Another option would be to echo (although not slavishly follow) the route of the Gospel Oak - Barking line (from Walthamstow, i'd suggest Whipps Cross, Leytonstone, Forest Gate, Barking); this would allow that line (well, as far as Blackhorse Road, anyway) to be taken out of passenger service and dedicated to freight use, which would be useful. However, this is a bit of a round-the-houses orbital route, and probably not much use to anyone at all.
The Croydon idea's a winner, though.