In reply to George Ormerod:
The 2 main brands in this area are Garmin and Suunto, I don't know anything about Suunto models.
For Garmin, the models which have a barometric altimeter are not that many - Vivoactive 3, Forerunner 935 and the various models in the Fenix 5 range ( 5, 5s, 5X, 5 Plus, 5s Plus, 5X Plus ). Those are current models, there are some older models that you may still be able to find new, or definitely 2nd hand, mainly Fenix 3 I think ( note there was no Fenix 4, it jumped from 3 to 5 )
The Vivoactive 3 only has 1 button, lots of functions are touch screen which I personally don't like on a sports watch, too easy for sleeve cuffs, or even rain drops, to cause problems.
The Forerunner 935 is designed as a triathlon watch, and is effectively a Fenix 5 in a plastic case ( as opposed to the Fenix's metal casing ). It's quite a large watch !
For the Fenix 5 models, they come in 3 sizes :- 5s is smallest, 5 is medium, 5X is large
Functionality wise the 5s and 5 are similar, except the 5s has a smaller battery and therefore GPS time The 5X has proper mapping capability ( rather than just breadcrumb trail ). Then they introduced the Plus versions of the 3 models which added music, Garmin Pay, and mapping to all 3.
All these watches I've mentioned are smartwatches, so can pair them with a phone to see emails, texts, call details, etc, but you can choose not to pair, but you are paying for it.
So in summary, the smallest Garmin GPS watch with a barometric altimeter is the Garmin 5s, but if she's into long ultras or Ironmans then battery may not last long enough ( think it's officially 12-14 hours )