You could go from South Acton or Acton Central on the Overground to Willesden Junction, and change there for Wembley Central. (The Wigan pubs are closer to Wembley Park on the Jubilee line from Bond Street.)
Journey time 25 minutes, fare £4.50 (£1.50 with an Oyster card).
Acton stations are in Zone 3; Wembley stations are in Zone 4. You could get a Day Off-Peak Travel Card for Zones 1-4 costing £8.00.