There's a couple of issues here
Recruiters calling you means nothing. Absolutely nothing. It's like saying "I received some spam in my email".
In answer to your most direct question, give your notice when you want to. The upcoming travel is totally irrelevant.
"it's also gonna appear that I'm someone just trying to avoid this travel that none of us seem to want"
This is confusing. The business travel is in fact a perfectly good, indeed excellent, reason to resign. You or your colleagues would say to your boss "I'm resigning because I don't want to do those trips." Very simple.
(Obviously you don't have to give any reason when you resign. State the words "I'm resigning." But dislike of the trips is an absolutely good reason to resign.)
It is absolutely commonplace that managers hear things like "I'm resigning because the travel is no good." That's a normal and good reason for resigning.
- You're going to quit without a new job to go to. There are a couple issues here:
4a. You mention that you got some recruiter spam. This means nothing. It could be that you can easily get another job, but, the recruiter spam has no connection one way or another.
4b. As a rule, don't quit until you get a new job. Why would you? Just keep taking the money until you secure a new job.
4c. There are exceptions to this. For software engineers, the market is so hot that you have to reconsider the rule of "don't leave until you have a new job". For programmers, if your speciality is in demand and if you are good and if location is not an issue, there are distinct advantages to "just leaving" and then choosing a new job. The two advantages are folks hiring programmers want them now, now, now; if you're aggressively ready to go see them and indeed start "anytime" it's a huge advantage; secondly, having quit your previous job is a huge mark of confidence, it means you know exactly what you're doing and you're not "just looking", you know what you want.
- Commuting. Commnuting is hell. It sounds like in short you dislike your current job (due to the travel) but you're stuck with it due to the location issues. Could it be you in fact have t move to resolve this issue? If you're trapped you're trapped. Commuting for hours is a non-starter, so, ... is the only solution moving?
We now know that our OP is a software engineer. In today's market it is almost certainly the case that she can now change from on-site employment to fully-remote employment.
This completely solves all problems:
- OP can still live in the unusual/remote area
- No commuting (at all)
- Escape the current "business trips" company