You can start here:
See if this one is suitable for size and price.
Panasonic ZS20 (TZ30) .... USA(Europe)
Price is about $230 USA
Could someone please suggest some options for budget, slim point and shoots with built-in gps?
Built in gps is the essential feature for me (I don't want to carry a gps accessory).
The smaller, the better.
Optical zoom near x10 would be a bonus.
I'm not fussed about getting the best optics or the most functions.
By cheap, I mean ideally less than ~ $325/€250/£200
I'm having a really hard time searching. I can't believe how terrble the search filters are on manufacturers and retailers sites. They often don't seem to have price and gps as filter options.