Good news and bad news.
I have a similar sort of Sony (PCG-R600). They are so vastly incompatible with Linux that I have been trying different distros for at least 5 years and I have had virtually no success. That is the bad news.
The good news is that I have had some success. Crunchbang LIte (a Ubuntu based distro) is the ONLY Linux distro that I can successfully install and run on that machine. So at least you don't need to spend ages thinking about which distro to choose http://crunchbanglinux.org/
According to another thread they have a new version coming out soon as well.
If you do decide on that then I suggest the Lite edition as opposed to the Standard (unless your Vaio has much more ram than mine).
Fujitsu Lifebook AH532 Laptop. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Ubuntu12.10 (Unity), Mint14 (Cinnamon), Manjaro (Xfce).