Don't get stuck on location. There's no faster way to find yourself storing your precious memories in a facility that sucks than to get stuck working with the one that just happens to be closest to you or cheapest in your community. Cast your net wide enough so you have a good handful of options that you can investigate.
Check the reviews. Look up the storage facility on Google. You obviously want to take reviews with a grain of salt, but if they're all bad or there's a recurring theme, you may want to steer clear. The reviews can also give you some insight into what you may want to keep an eye out for if you go visit the storage facility.
Compare the gate and office hours. A number of storage units only post their gate hours, to make the location sound like it's open later than it really is. Remember there's a difference. The gate hours are usually the hours in which you can access your storage unit, but the office hours are almost always shorter. If you have a problem or need to speak to someone, you'll only be able to address your issues during office hours. Similarly, make sure the gate and access hours are convenient for you. If your storage unit closes at 5pm on Saturdays and Sundays, it's probably not very convenient, and there may be a reason why.
Ask the property management if you can see the unit you would actually get. This, or at least a unit on the same floor or in the same area. Some storage facilities will show you a clean, 3rd floor unit but actually rent you a dirty, bug-infested basement one, so be assertive if you have to so you can see a unit representative of the one you'll actually sign for.
Ask if there are any rental specials or discounts available. Most storage companies will offer you the first month free or for $1, which makes the transition from an old storage unit to a new one really easy (especially if you've already paid for the last month in the old unit) or if you want to make moving into the new unit a little less painful on the wallet. If they don't offer a special, don't worry, the next one you visit probably will.
Find out what happens if you miss or are late on a payment. In many places, storage units aren't treated like apartments. On the first day of the month, your rent is automatically late. Grace periods vary by the company or even by the state, and in some cases even being a few days late with your payment means your unit's contents can be auctioned off to the highest bidder at a wholesale auction. The last storage unit I rented gave me that scare tactic, and reminded me that I should always be timely or else the unit would be scheduled for auction and I would incur daily late fees. Make sure you know what your storage unit's policy is before you're stuck trying to do a wire transfer or pay online because you left town without dropping off a check.
Hopefully, this helps you to find the perfect storage unit possible and hopefully that storage unit is ours!