Property in state A. Can I make an LLC in state B own it with minimal hassle? (not doing any business, just holding the property)

I have property in state A I want a new LLC in State B to hold. The LLC wouldn't be doing any business or have income. If I want to get maintenance on the property (not lawsuits) would the companies I deal with need to go through the registered agent for any reason? Would the LLC need an EIN or bank account?

Probably not a problem, but I'd check w/ the state you want to register in (delaware or NV are good choices). In most cases, you just need to have a registered agent in the state you want to register in, as you said, but there's no requirement to use the RA for anything other than court summonses and such.

There are a couple of issues you need to watch out for:

Transfer of the Real Estate
You'll need to transfer the real estate to the LLC for fair consideration (not for free or $1) for the IRS to be ok with it. You can do a tax-free exchange but this requires some tax assistance to be one properly.
In addition, you'll need to transfer the deed over in the name of the LLC in the county recorders office in the county in which the property is located to give creditors notice that the property belongs to the LLC, not you.

Foreign Qualification
Depending on how much "work" is actually done on the real estate, the foreign LLC might have to "foreign qualify" in the new state because it does 100% of its business there. This is an additional filing.

Disregarded Entity
If you are the only owner, you can use your social to report taxes on Schedule C and not get an EIN for the LLC. However, many banks require to open a corporate account that the LLC have its own EIN. No bank account is necessary if you do not plan to do anything with it though.

Note: This is not legal advice nor does this create an attorney-client relationship.

"If I want to get maintenance on the property (not lawsuits) would the companies I deal with need to go through the registered agent for any reason? Would the LLC need an EIN or bank account?"

You would need a registered agent in order for the LLC in state B to foreign register in state A and thereby hold property in state A, unless state A is one of the few states that provides registered agent services through the secretary of state's office (i.e. New York). If you are going to pay for the maintenance on the property, a company bank account is recommended to make the transaction. EIN, as its unabbreviated name implies, is more relevant if you hire employees but as Alex mentioned, banks may require the EIN in order for you to open a company account.

Interesting strategy you have here... :)