I'd probably go with a light backpacking boot. The terrain is pretty rugged, so maybe something a bit heftier than a dayhiking boot, although something like that may well work.
A good example of a boot that's about the right weight is the Keen Klamath ($150). They're a light backpacking boot with waterproof nubuck leather and waterproof/breathable liners (thunderstorms could be an issue). Lots of traction, very comfortable. They'll feel more like running shoes than boots.
I also like the Scarpa Kailash ($170) a lot. I've worn a pair for a couple of years and they're one of my favorite hiking boots. They have light, flexible leather uppers, toe bumpers for protection, Gore-Tex booties, a great fit. Available in both men's and women's sizes.
For something pretty tough but just a bit lighter, I'd suggest a pair of Oboz Sawtooth Mids ($135). They have fabric and leather uppers, a waterproof membrane, and a nylon shank for pretty good stability. I've been using a pair this summer and am very impressed by the traction they afford. Or take a look at the Merrell Chameleon 3 Ventilator Mids ($150). These are practically molded over your feet, offering a very low-profile, which is great when scrambling around rocks and gullies. But they still have leather uppers and and Gore-Tex XCR booties.
Have a great trip! It should be lovely then—warm, but not excessively hot.