Neighborhood to live in between Westminster and Egham Hill?

Hello! My husband I are will be moving to London in August 2015 for graduate school - he at the London School of Economics in Westminster and me at Royal Holloway in Egham Hill. We're looking for suggestions for places in between our schools to rent a one bedroom flat that will divide our commute relatively evenly. Anyone know of good starting neighborhoods we can look - hoping for somewhat reasonable rent, walkable (no car needed), preferably with the basics nearby - groceries, coffee shop, a couple restaurants or bars - between central London and Surrey? I've been looking at maps but have a hard time judging distance/commute time, and it's difficult to get a sense of neighborhood feels.

Thank you!

What do you consider is reasonable?

Oh, I suppose reasonable to the neighborhood. Because we're not leaving for a while and working full-time until the move, we have some flexibility in how we'll be able to budget. We'd prefer to stay at or below 900 pounds pcm but could swing 1100. We also have two cats we're bringing, so we realize our options are further limited by that.

Take a look at some estate agent websites,  or sites such as Zoopla or rightmove.   This will give you an indication on prices and amenities. 

Yes, I definitely have been. Thanks for suggesting Zoopla, I'll check that one out too.

However, most of the real estate websites are sorted by borough already without saying much about the actual borough itself, so I'm having a difficult time knowing what/where to search. I've been doing some guess-and-Googling, but that feels frustratingly inefficient, and still doesn't yield much about each neighborhood's qualities or ambience. I guess I was hoping someone might have knowledge of the geographic area between Egham Hill and Westminster and be able to make a recommendation on livable areas somewhere in the middle.

Look at Twickenham, clapham junction, and Vauxhall... maybe Staines as starting points.  Commute costs may be a consideration as well.  Remember that the tenant is responsible for property tax (called council tax) which will easily add £100 a month on top of the rent price.

You will have options with cats (so bring them!) but it will GREATLY reduce your options.  Use the internet to get a feel for properties but be VERY flexible when you arrive.