The tubes and rail should be fine.
I think the best way to get there is either on the train to Charlton station (right outide the ground, served by Waterloo East, London Bridge and Liverpool Street) or on the Jubilee line to North Greenwich (a bit further away, but easy enough for pubs and the tube runs every 3-4 mins as opposed to every 15-20 mins for the train).
I've been recommended a pub called The Pilot Inn (SE10 0BE) near to North Greenwich station which is supposed to have good food and a full selection of Fullers beers. Where's everyone else going?
Not sure how up to date it is, but this is the advice from footballgroundguide.com:
Simon Phillips informs me that 'The Antigallican, a big pub near Charlton station, seems to be the favourite haunt of away supporters'. However, it can get very busy and this is not helped by the local Police not allowing fans to drink outside. It is a rather basic pub but has real ale available (albeit a lone handpump) and also offers a selection of filled rolls and pork pies. Whilst Colin Gilham recommends the 'Rose of Denmark' on Woolwich Road. The pub not only allows in away supporters but absolutely welcomes them. They have a photo display on the wall of fans from visiting clubs that have frequented the pub this season and it also has SKY television'. Please note that this is a home supporters only pub after the game. To find these pubs come out of Charlton station and turn left into Charlton Church Lane and the Antigallican pub is down on the right hand corner. If you continue down to the t-junction with the Woolwich Road and turn left you will reach the Rose of Denmark further down on the left.
There is also the Charlton Liberal Club, to which away fans are welcome on payment of an entry fee of £1. This is more spacious, less busy, has a large screen television and families are welcome. The club can be found by turning right out of Charlton station and walking 300 yards up the hill on the left hand side of the road, past the row of shops. The club is a five minute walk from the away end, but like the Rose Of Denmark, it becomes a home supporters only venue after the game.
Robert Taylor adds; 'I would recommend the Pickwick on Woolwich Road, which is about a 10 minutes walk away from the ground. It has a good mix of away and home fans, with a friendly atmosphere (with the usual banter!). There is a huge beer garden where kids are allowed to play football and it has Sky television with a huge projector screen at one end. It has a pool table, games machines and there is a handy chippie right next door'. Alternatively alcohol is available in the away end.