Thai Square Putney is the classiest drinking place to go in Putney by far. The staff are friendly, it is layed out nicely and the drinks arent overly priced.
Thai Square Putney overlooks the Thames and at night it is breathtaking. The only problem is the jealousy of the women, be prepared for that. Instead of staring, they need to head down Harvey Nicks!
I would reccommend Thai Square Putney as a starting point before going to the West End.