...Continued (my phone doesn't handle long posts well)
Basically, you'll find your way to all the daytime sights easily enough so there's no point worrying about being really close to any of that. But if you want to see some night life, choice of location becomes more of an issue as you may not be as happy navigating your way around.
Still running with the assumption you want to see some nightlife of course. First up, Piccadilly and Leicester square- don't even bother. Overpriced, shit music, lots of twats, good chance of someone relieving you of your possessions.
Soho is a bit cooler and more pleasant, but it's not that great.
I'd still recommend Shoreditch and brick lane. Shoreditch isn't as trendy as it was and there's more drunken arseholes than there used to be. But it's got plenty of live music and DJ nights and still probably your best chance of catching some guy tweakng dials on a laptop without necessarily going to a big dirty, drug fueled nightclub. I can point you direction of those too, btw.
Camden isn't bad either. Still mainly an Indy rock sort of place.
Farringdon is pretty nice for pubs, small bars and one enormous monster of a nightclub.
So I'd start looking around old st. It's a short walk to the work thing, and a large chunk of decent nightlife. I agree with the premiere inn suggestion. As cheap a "proper" hotel as you'll find. Rooms are always decent enough. http://www.allinlondon.co.uk/stayinfo/s ... how=345563