The V and A houses a public collection of prints and drawings of every kind imagineable from old master drawings to photographs, playing cards, fashion plates and wallpapers. You have to select what you want to see from the collection http://collections.vam.ac.uk/and book in advance. The behind-the-scenes route up to the study room of v and a is a treat alone (pictured)
In between soho and covent garden. There ares lots of great independent shops on this street. Dover bookshop, magma, super superficial and Mint to name a few. Also if you want a cheap lunch on your work break Cafe No.1 is amazing. £2.50 jacket potatoes with cheese and beans.
Slightly biased as this is where I live, but Stoke Newington is great place to spend lazy saturday / sunday afternoons getting sloshed with friends. There are 10 + pubs within walking distance who all are great places for one reason or another. I'll pick out the White Hart for its huge beer garden...
East london spot with a bit of everything, food during the day and cocktails, music and cinema during the night. Few nice places around like E5 bakery, Netil 360 rooftop, and Mare Street Market