Look at storage units near you, many have outdoor space for rent. Then call your insurance and give them the address and maybe a copy of the rental agreement so you can keep insurance at a much lower rate.
Digital Nomads
Here in Chicago, we have Spothero which allows to set up parking for one night or by the month. I'm sure your city has a similar app. Also Craigslist posts a lot of parking options for the long term.
In colder states, people sometimes have “summer cars,” so look for places that offer winter storage.
Do you have any trusted friends/colleagues where you are? Maybe I'm just thinking of this from the small-town perspective where I live, but if someone I knew needed a place to keep their car and have someone at least occasionally crank it and drive it a little for them, I'd for sure offer to do that. The absolute worst thing for a car is to just let it sit.
I did this when I traveled abroad for 6 months. Rented a storage unit that had outdoor access and backed my car in. Both were large SUVs and a bit tricky to squeeze in but made it. With todays prices I’m guessing it’ll be 120-200 a month
A couple years ago, I used Avail car sharing out of the Denver airport while I was out of the country for 3 months. It’s a program run by Allstate, so it’s fully covered by their policies when your car is with them. If you’re comfortable with someone potentially driving your car occasionally, it’s a great option. You get paid (a small amount) each day it is used, and more importantly (for me, at least) free parking at the airport. My return date kept changing, but it was super easy to change that as well. Worth looking into as long as your car isn’t a super beater.
Just so you know, I did this and the battery was completely flat when I got back.
Use battery discharger
Use neighbor.com for affordable car storage long term. And be sure to add fuel stabilizer https://www.amazon.com/STA-BIL-22214-Fuel-Stabilizer-Fluid_Ounces/dp/B000B68V6I
If you don't mind it being outside, storage places charge about $20-50/month. If you wanna store inside, garages are wayyyy too expensive. So I did Public Storage and got their 10'x20' and parked mine in and put it on jacks for about $130/month
Why on jacks?
Keeps the tires from developing flat spots
Thanks for all the suggestions, everyone. I'm going to try and find a friend I can leave my car with so they can run the engine like once or twice a month. Otherwise will probably look into the variety of storage options you guys mentioned.