I recommend two options:
1. If you aren't really a "photographer" but are actually just a fancy tourist mostly interested in snapshot sharing and social media picture exchanges, then an iPhone camera will serve you as well as you probably could have done with a full "pro-quality" DSLR from a few years ago.
2. If you are a creative photographer who takes pictures intended to become wall art (for yourself or for others), then an OM-1 with the 12-100 f4 will serve you well in most travel environments. If you augment that with the 8mm f1.8 fisheye, you'll discover you have a low light wide angle capability to serve you extremely well in challenging architectural environments. (The Olympus fisheye lens can be "de-fished" very effectively using OM Systems software, or even in-camera software.....so don't be put off by the word "fisheye".) Lastly if you are a serious wildlife photographer, you could (should) add the (expensive but extremely good) 150-400mm zoom. It isn't lightweight by "cell-phone" photographer standards, but it is very lightweight by fancy wildlife professional standards and it can outperform most wildlife professional photographers...... best of all, those three lenses can be easily taken to wherever you might like to travel, even into extreme arctic/antarctic/safari/helicopter etc. environments. And if you forego the 150-400mm you'll discover everything can fit into a simple bellypack (along with spare batteries, extra memory cards, bottled water, and travel documents...... I can (have) gone 3 weeks into exotic places with nothing more than a simple backpack and my bellypack. (and a bunch of money to tip guides etc. ... :-) ) Enjoy,
I was north of Svalbard on a ship when I saw some professionals getting better pictures than I with a much smaller rig. I was using full frame Canon, they were using Olympus. I've since sold all my (expensive) Canon gear and converted completely to Olympus. I've got the EM-1.3 and the OM Systems OM-1. I've also the BWL, the 300mm f4, the 12-100, the 1.4x and 2.0x extenders, and assorted other lenses that aren't relevant to your question and style of photography. I've had the Panasonic 100-400mm but I got rid of it (too soft) and I know from other people's experience that the Olympus 100-400 is better than the Panasonic, but it too suffers at long ranges. Based on my experience, you might consider a used EM-1.3 if you want to keep total costs down. There are quite a few of them out there (mine included shortly) for sale because people (like me) have moved up to the OM-1. I love the OM-1...especially for BIF. The AI subject detection is fabulous for birds, and when you use any Oly lightweight lens you can slew the camera rig around hand held for very fast action....particularly when shooting from ships. My recommendation is get used stuff to keep inside your budget. But, get the OM-1 if you can afford it after getting the 300 f4 and the 12-100 PRO. Add the 1.4x for some extension on the 300, but don't go for the 2.0x. The 12-100 will be on your camera all the time (except when you are doing wildlife/birds). You'll really like the OM-1 performance (if you can get it inside your budget)...but the EM-1.3 is pretty darned good too. No question you definitely want the 12-100 and 300f4. Don't skimp on the glass. You'll definitely be able to see an IQ degradation if you choose something else....Other lenses are good (don't misunderstand me), but these two are noteworthy. I know that lots of people demand zoom at long ranges, I like it too (that is why I have the BWL), but that is out of your price range and the 300 f4 is going to stretch your budget as it is....but you said you pay close attention to IQ. Therefore I'd suggest you definitely get the 300 f4. It (with the 1.4x on occasion) will keep you satisfied. Later, when the boss gives you permission, go for the BWL....but you'll need to be very very good to the boss... LOL.
Search online for Smoky Mountain scenes... you'll get plenty of advice
lots of choices. Taking her to a camera store might be a good idea. However, everyone has their biases including the camera store salesperson. My biases: Get involved in a camera line/system that offers high quality, low cost, light weight, excellent performance. In other words, consider an iPhone. If she wants the flexibility and power of a purpose built camera then consider Olympus Pen-F. If she wants truly high performance, then forget Canon, Nikon, etc. Go for a medium format camera. Personally, I used to be a Canon user, I find the Micro Four Thirds format is more than capable of doing everything that any dedicated purpose built photographic line can do. Moreover, the gear isn't anywhere near the price range of the FF camera lines, it is lightweight enough that it is a camera more likely to be with you when you find that "great image". If one truly buys into the idea that there is something "wrong" with anything smaller than a full frame sensor, then that person should be using a medium frame sensor. Full frame capable systems are simply too heavy/costly for most imaging when compared to equally capable smaller sensor devices. The iPhone can be a good learning tool for composition. MFT will be a good lightweight/high performance tool for all but the most extreme imagery demands, and for those cases one should bypass Full Frame and go directly to Medium Format sensors.
Me go shooting ... Me do good ... Me teach grandson how to speak English. Him not doing good with grades ... him never get good job. So glad me taught him to speak...