I personally wouldn't recommend Leicester Square to any friends. Although they've just finished a project to make the actual square nicer, it's not the most 'refined' of places, especially at night. You've got big cinemas, lots of night clubs, a few casinos, plus fast food places and chain restaurants.
Le Méridien Piccadilly is the Starwood I'd probably go for. Very nice since the recent refurbishment. I personally like the Firmdale hotels in London best.
What to do depends on you really and also what day of the week you'll be visiting. But certainly try to take advantage of some of the fantastic restaurants in London. Some of the pre and post theatre offers are very good value. I'd also see if any shows are in town that you want to watch - London has some fine music venues and great acts passing through.