High on Zoe's list has been an area called Weybridge.
It wasn't too difficult to get there, or to get back. The trip starts from Waterloo station, which is always a pleasure to use (and a chance to feed a hangry Zoe). It was clear that there is limited train coverage on the weekend, however.
Weybridge itself had a fairly old-timer feel. It's a small town, somewhat tourist-y. There are a number of beautiful homes to look at, if you're hunting.
There are also a few nice restaurants in the town. The town itself has most of the basics. It also has moderate-to-high traffic on a Saturday afternoon. There were a number of buses going through it to take you to the surrounding residential areas.
The bottom line for Weybridge for us is that prices are very high for houses, and it offers little in terms of apartments. We therefore added a part 2 to our visit, by taking a bus (which was stupidly expensive - seriously, an über ride would have been much cheaper) to a neighbouring area called Walton-on-Thames.
This had a different vibe. It was a more modern town, with modern amenities. It had a large shopping strip, a mall, and higher amounts of car traffic. Housing there is more affordable, but the area has zero charm.
Oh, and it was so cold that my iPhone died. It only came back after warming up in my pocket for a while.