Texting isn't necessarily my strong suit, so maybe the other guys have some thoughts but here are my two cents any way
1. What's a good general frame control for this situation? I don't wanna be a guy dancing to her tune
This is a classic texting moment where you ask her a question and she doesn't answer it and instead asks you a question that essentially puts you in a position to qualify. Definitely don't just throw out an idea, that makes it simple for her to reject the idea. Instead I would do a bit of a yes latter to A: sus out some logistics, and B: Get her to invest more
So something like
Her: liiiike?
You: Good question Abbey, well, you're an adventurous person right? (basing this on all of her hiking photos, you could say creative person, or lowkey person, or whatever suits the situation)
Her: Definitely adventurous
You: Yeah you are, I seen that cliff you were climbing. But hey, what exactly is your schedule like. We might not exactly have the time to climb Everest this weekend
Her: Lol true. I pretty much have school in the days and some studying at night, but i have time here and there
You: Right on. Toss me your number and we'll come up with a good time. I know a great adventure
and so on
This is just a rough template but the idea is to not just play into her "tell what you have in mind and I will decide then" frame.
2. What are some good options for someone without a fake ID?
Anything that allows you to have smooth logistic momentum. Use the classic 3 bounce date structure.
1- a place where you can meet and greet. A coffee shop, and ice cream shop. That sort of thing. Somewhere where that will make it simple to move the date once you have had a chance to meet. So no where where you will be locked into some big activity (this includes sit down restaurant) that will kill momentum.
2-A place that you can move to as momentum builds, this is where you are going to start to deep dive, or run some gambits and all that. Bookstores/libraries, parks/beaches. Those sorts of places. Again, don't go somewhere where you will get snagged in a huge activity (like a hike or something). Something light and fun and easy to move from when the moment calls for it.
2- Your place, or wherever you plan to escalate. This should be a place that is easy to move to one you have built momentum and seeded the pull. Remember to offer a bit of plausible deniability when you suggest it "Hey, I gotta charge my phone, let's stop by mine and I'll show you that painting I am working on"
Obviously, dates are dynamic and you have to improv, and sometimes you have to skip a step or, or hang out a little bit longer than anticipated, and so. But this is a good basic structure. And the truth is it doesn't really matter exactly where you take her as long as it is simple and easy for you to both enjoy each others company.
Just try to make sure, that each location is relatively close to one another so you don't get trapped in a bunch of travel time that kills momentum.