The only place we had a chance to buy souvenirs was at Port Lockroy. and is the only place as far as I know. If you land there and they are open you will find all kinds of stuff from hats, t-shirts, mugs, patches, etc., etc. Also, in Ushusia, you can also find lots of stuff with Antarctica on it...Port Lockroy, to my knowledge, is also the only place you can mail post cards. Depending on the time of year, it may take months for the cards to arrive at their destination since they have to go to the UK first and it also depends when a ship may be leaving the port when not iced in..We mailed some in February 2011 and finally received them in November 2012!
This is also a place where you can get an Antarctica stamp on your passport which is available just outside the gift shop.