Is she a tech head? Does she like the idea of interchangeable lenses? If so, get her a K70 then every birthday buy her the lens you want but can't justify, then borrow it
If the K70 is too big have a look at the Olympus pen range as an alternative to the ubiquitous sonys. They are nicely built and perform well. Also adapters are available
Eschewing interchangeable lenses, bridge cameras give you a great zoom range. My Fuji Hs20exr had 24-750mm equivalent and the Fuji he range are great and within your budget, but they are DSLR size.
A smaller bridge camera is the Olympus Stylus 1s. Tremendous quality, it feels premium. Great sensor, same as the last Pentax Q, great lens, f2.8-f8 from 24mm to 300mm equivalent, raw, manual and all the modes you need articulating screen, WiFi, tremendous evf. I have one and think it is wonderful, so much so I am taking it with me when I am off on a short break while my K3 gets some well earned rest. The Olympus is not pockatable thanks to the evf but it will slot in a bag nicely. Tip, get the 1s over the 1 as you get better battery life.
The Olympus is slightly larger than a compact but has a tremendous zoom range thanks to the sensor size. There area also several tremendous compacts with all the modes that have a bigger sensor but lose out on the zoom range like the Ricoh gr ii and the Sony RX100
Happy hunting