What model jeep do you have? You said it needs work. Normally I’d say get rid of it. But, it might not be sellable?
Way back, over 20 years ago, when I was renting, there was an on-site manager who wouldn’t even lwt me check tire pressures, let alone pop the hood
But he let people that didn’t even LIVE there put their trucks on jack stands and overhaul the rear end 
When I finally bought my house, I turned in my apartment keys and never looked back 
If there’s one thing I learned, it’s this . . . you want to have your own property . . . and not in an hoa . . . so that there’s never a situation where your neighbor can forbid you from working on your car
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The only public space job I ever did was the front brakes of a … wait for it … Yugo. Some poor broke woman who worked as a dishwasher for my wife at the time (restaurant business). She was so hard up I had to help her. To her credit, when the brakes went metal on metal, she did just pull into a parking space and left it.
It was a combination gas station / mini-mart / deli. I know it would sound weird to call such a place “higher-end”, but it was. Fancy sandwiches and salads from the deli, and all manner of local and organic whatever in the mini-mart. To their credit, I asked permission and they granted it.
As for the storage unit discussion above, the issue isn’t about legal or illegal. I don’t think that there are any states with laws about it. It’s just company policies for whomever owns them. So the OP might keep looking around for a place that does allow car work. If I owned one…I’d probably say no. Or maybe I’d have just a few spaces where it was allowed. Most people, I’d think, would not want to store their stuff in oil and grease stained places from past car work.
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Below is a long yarn about removing a transaxle in a rented storage unit.
Doing Clutch Replacement in Walmart Parking Lot - Maintenance/Repairs - Car Talk Community
If you are going to do major engine or transmission work you really need your own garage. I never did major work just general tune ups, brakes, etc.
I used my folks garage when at home. At school I used the street, residential and trailer park for a summer. For a while I rented a room for $5 a week from a widow. She let me use the garage if I shoveled the sidewalk.
In our apartment a garage cost an extra $15 a month and had lights and an outlet. At one point I had three different storage garages rented but none of them had lights or power. Plus some cities and covenants don’t allow major work anymore. In my houses, a good garage has always been important to me but the major work goes to a shop.
So it’s tough for a do it yourself guy without a home. If you join the army, most bases have a hobby auto shop but that may be a drastic solution.
I worked at company that had a beautiful 30 acre site. Very expansive building design. Had a long row of garage stalls for storage. No idea who designed it but we could work in storage units on stuff. Was built in the 60’s. Company bought newer, nicer complex 5 miles away and sold old site to developer who completely tore it down. Has new homes on it now.
That and the idiots doing body work/paint. Some yokel was sanding his bondo job and the dust went everywhere. Many storage buildings where I was renting are not completely sealed between units and stuff from one unit can pollute the others…
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Out of curiosity, after reading so many good suggestions, I decided to call a couple of the self-storage facilitates in my area of Hampton Roads Virginia. I told them I want to store my car and perform some minor work on the car while it is there… I did not say, nor imply that I wanted to tear my engine down.
They both told me I would not be allowed to work on any vehicle while it is on their property. I asked why and they explained that there is the possibility of fire due to the use of cleaners, degreasers, and open containers of fuel. Additionally, there is the real possibility of oil stains getting on the floor and getting those stains up is near impossible and no one wants to rent a facility with stains on the floor or smells like an old garage…
I am lucky in that I am retired military and I live with 10-miles of an Air Force Base and an Army Base and both offer automotive hobby shops, fully furnished with tools, hoists, with storage facilities while awaiting parts. It’s not free, but reasonably priced.
So, as suggested, if the OP insists on performing their own repairs, look for an old Mom & Pop service stations that only sells gas now and the bays are no longer used and they might be more than happy to rent out some space…
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Yeah I’m one of those idiots that did body work in every garage I had access to. I only painted in my own though.
When I was in the Army it cost me $0.25/hr
I knew a guy in college that completely rebuilt a Harley in his dorm room. I don’t think anyone complained. But I hope he waited until outside to start it up!
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I remember those days; unfortunately, like everything else, inflation has raised the cost ant the “Auto Skill Centers” (formerly the Auto Hobby Shop)… the auto lift is $3.50 an hour, an inside stall with a fully stocked tool box is $4.50 an hour for the first 2-hours or $10 a day… outside storage is $3 a day… they also have independent professionals on site that you can subcontract at $80 an hour. Or you can ask the person in the next stall for help (Free…). L 
L . . .
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A garage is where that type of work belongs. This is about storage facilities.
I hate to inform the people you talked to, but you don’t have to work on a vehicle for it to leak fluid(s) on the floor… 
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Mike’s cost works out to $2.12/hour now.
We all know that some vehicles are not completely “housebroken” and do drip a bit but it’s not like when an engine is broken down and oily parts scattered all over the floor or someone changes the oil and the drain pan is not quite positioned correctly and a quart or more of hot oil is running all over the floor. And then there are these folks…
Darwin award winners? 
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Real mechanics know how to remove grease/oil stains from concrete floors.
We don’t worry about piddly crap like that.
Tester
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Tester beat me to it!!!..
Heck when I was pulling or installing at least 5 transmissions (fwd, rwd, awd, 4wd didn’t matter) a day, we had to clean every drop of fluids before moving to the next job, even the trail going from the bay to the build room, and if a big mess, you had to stop and clean the mess as soon as it happened to keep it from spreading to much, and every Friday we shut down at 3pm to clear and scrub the floors down, the air hoses and light cords racks etc, you could eat off the floors they were kept so clean… And the boss(es) was right there with us… lol
And no, nothing special covering the floors, just kept clean…
Reason, the boss/owner wanted to be able to bring a customer at anytime out to the vehicle to show them what was going on if they had any questions or needed to get something out of the vehicle…
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For the DIY’ers who work on their own vehicles and get stains on the concrete, the best advice I can give is, buy a brake cleaner that contains xylene and a bag of oil dry. And if you can’t find a brake cleaner with xylene, you can purchase a can xylene at a hardware store..
Apply the xylene over the stain and let it sit for a several seconds and then apply the oil dry. Let that sit for 5 minutes and sweep up. Repeat as necessary until the stain is gone.
This guy is using shop towels to absorb. But the principle is the same.
Only with oil dry. it can be used over and over again until it no longer absorbs anything.
Tester