Since you've gone AirBnB, this is a bit of a problem.
Generally, the hotel's issue is that the room is not ready for you.
Talk to the hotel and ask them what your options are. Certainly they will cheerfully store your luggage, and may even put it in your room for you once your room is ready, so you can simply arrive back and collect your keycard.
As for freshening up, they may also have solutions for you there. If the hotel has a fitness center, it's an easy fix. Or they may have a relationship with a nearby gym, they may be able to get you discounted or free access.
It certainly won't be the first time they've encountered the issue.
AirBnB, cheap motel or other BYOservices
I don't see any probability of getting "freshening up" services in the same place as "luggage storage", outside of renting a hotel room, which kinda defeats the purpose of airBnB. So you'll need to do a fair bit of "running around" to get these separately, which will really bite into your day. Which means location will matter. And AirBnB's are often out in residential areas where services are different.
First, can you rent a car, at least for the first day? Put the luggage in the boot; done.
Second, look at Private Mail Box / Shipping Assist companies such as Mail Boxes Etc. They shouldn't mind storing your luggage, and they have lots of locations in residential areas where your AirBnB might be.
As far as "freshening up", I travel Amtrak a lot, and my style is "spongebath in the washroom" - and mind you, I am typically sweaty from having hiked all over Chicago during the layover. So I would just do that in any suitable public bathroom, in a little-trafficked area where the whole bathroom can be locked. Note that I bring all the "kit" to do this, including razors, washcloths and ziploc bags for the now-wet washcloths.
However if you want something a little more upscale, find a gym/fitness center - any of them will have a single-day rate for carte-blanche access to the facilities, including locker rooms. You can even swim or work out while you're there. Bring a lock. The gym will NOT have room to store your luggage, so you still need to solve that other problem.
I can see where this might not appeal. If you need the pampering of a proper hotel bathroom, then they have hotel day-only rates, which will let you solve both problems at once, though, at the highest cost.
Honestly, if you didn't have a car, the headaches of all that running around would "take the gild off the lily" for AirBnB as far as I'm concerned, at least for the first night. That's the problem - AirBnB doesn't have all the amenities of a hotel and experience at what travelers need, because hotels have been supporting travelers since they turned away Joseph and Mary.