I've been invited to open days at the Universities of Warwick and Manchester (both for Maths & Philosophy), one day after each other - Warwick is on March the 2nd, and Manchester on the 3rd! I'm planning to ideally travel to Warwick on the first of March (I live in Hayes, Middlesex), spend a day in a hotel there, do the open day, then travel to Manchester and do the same before getting back home to London.
I'll probably be on my own the entire time - neither of my parents are available during this time, and although I could ask a relative to accompany my, I'm quite excited by the prospect of such an adventure.
So what I want to know is:
1) How can I do this as cheaply (priority 1), conveniently and enjoyably (priority 2) as possible? i.e. train (which?), bus (which?), or if neither of these is viable, should I get someone to drive me (Id rather not, but it may be necessary if it'll save a good chunk of money)?
2) What B&Bs should I stay at and how much do they cost?
3) Is there anything else pertinent to this that it would be helpful for me to know?
Thanks a bunch in advance.