Let me first tell you that I agree with the Baby Jogger City Mini GT2, I mean, it's a quality pushchair that can cope with almost anything, including terrain and/or a very tall toddler. It's expensive, yeah, BUT you'll also sell it later on much better than a cheaper buggy - I mean, moms will gladly buy a used one as well. And you pay for quite a lot of features, starting with quality wheels and ending up with an adjustable handlebar. Just a thought.
Moving on, I would most certainly recommend a TFK Dot 2, which is a small buggy while being very capable even on terrain. It is, however, not available everywhere, so just look around if, by any chance... It should even fit the price tag.
The Cybex Eezy S+2 is a much smaller stroller - I mean, it's a travel stroller, which you say you're going to be doing (traveling) while having slightly larger wheels so it might tackle some light terrain for you for sure. There's no adjusting the handle but if you're not extremely tall, it should fit for the purposes you describe.
My next advice will be something smaller, like a Nuna Pepp Next. Different thinking would be a tall-handlebar-ed Quinny Zapp Flex Plus (nice amazon offer here) which is a reversible stroller even, and nice small folding while with chunky-ish wheels. Not the lightest but OK weight-wise and the fold is very nice and compact.
Please, do think that the price of the stroller matters a lot, meaning it will be reflected in the features, the materials and fabric quality, and the later sellability. It is economical and ecological to purchase a pre-owned pushchair in those cases the price is important (but the performance, too). And while traveling, you'll need something that is as light and small as possible - and EVERY pushchair will be able to tackle a bit of grass and unevenness if really necessary. So don't dwell too hard on the terrain capability and rather go for a light, quality option.