Use Whereis.com.au to navigate throughout Sydney and the surrounds. Penrith is the closest large shopping center with MYER and all the stores you could want. You can only get here effectively by Car or Bus, takes about 20min. Use the 131500:Transport Info website for bus timetables. Don't catch a train to Penrith... its takes FOREVER.
If you wont have access to a car, I would catch the train to Blacktown (30 min) or Parramatta (45min) Shopping centres. Blacktown is a bit bigger than Penrith. The train station is attached to the shopping center so there are no fears of getting lost. Its 2 levels and really easy to navigate your way around the shops.
Parramatta station is also attached to the Parramatta shopping center. The extra 15mins (if you can spare them) are worth it as the shopping center has 5 levels and is MASSIVE, everything you need and all the things you didn't realise you needed are there. You may get overwhelmed and lost track of time. I wouldn't reccomend going there the morning of the wedding. You need a whole day there.
Richmond itself has a small shopping center with hairdressers, clothes stores and the like. You can catch the train to Richmond for $2 and walk 2min to "Richmond Marketplace" and it's all there.
Oh and if youre going to use the Hairdresser "Panache" you can get there by train. Get on at Clarendon and get off at the very next stop, East Richmond. Walk across the train line and up along Burke St. then turn Right on Windsor St and walk 2 min and its the Pink Building with banners and signs everywhere.
If you have any other questions please let me know...