There are six Yorkshire sides in the draw but only three, Railway, Bradford and Huddersfield do not have to go to a replay.
Huddersfield will entertain either Carlisle or Grimsby at the Galpharm following their 3-2 win over Accrington Stanley on Saturday and Bradford, who beat Chester 1-0, have another home tie as they meet Tranmere Rovers.
Rotherham United and Doncaster Rovers will need replays to get through to the second round. Doncaster must beat Oldham first if they are to take on Crewe at home while Rotherham, who battled back for a 2-2 draw at Forest Green will travel to Swindon if they win their replay.
FA Cup 2nd round draw
Oxford Utd v Southend Utd
Swindon v Forest Green or Rotherham
Oldham or Doncaster v Crewe
Darlington or Northampton v Walsall
Cambridge Utd v Weymouth
Millwall v Barrow or Bournemouth
Stockport or Staines Town v Peterborough
Bradford City v Tranmere
Torquay Utd v Cheltenham Town or Brighton
Notts County v Havant & Waterlooville
Dagenham & Redbridge v Kidderminster Harriers
Port Vale v Chase Town
Leyton Orient or Bristol Rovers v Rushden & Diamonds
Huddersfield Town v Carlisle or Grimsby
Burton Albion v Barnet
Bury v Exeter City
Luton Town or Brentford v Lincoln City or Nottm Forest
Horsham v Swansea
Hereford or Leeds v Hartlepool
Harrogate Railway v Mansfield Town
Matches to be played over the weekend of 1 and 2 December.