What is the best way to find out the value of a small piece of a real estate?

First, you don't always have to own property in order to use it. You may get a personal (revocable) license from the owners or you may get an "easement" that goes "with the land" until officially extinguished. Second, you would get an appraiser and surveyor to look at the property and propose a boundary-line adjustment, not a "subdivision" that some people are yammering about. Finally, your LOCAL rules are the only things that apply for your situation. We can only guess. Your local attorneys will be able to help, once they have the deeds, survey and appraisal (of the land or the easement or the license) in hand.

Ask the neighbor if they're willing to sell. If they say no, it ends there. If they might be interested, there are some things that can make it not possible.

If the neighbor has a mortgage on the property, it can't be done. The lender will not allow subdividing.

If local zoning has a minimum lot dimension and giving up a piece puts the dimension on that side below the minimum, it can't be done.

As for figuring out a price, there won't be any comparables in the neighborhood for something like this, so the two of you will have to get together and figure out a price you can both agree on.

rather than buy the small part. Most people get an easement- written and recorded permission to use it for your driveway. It may cost a small amount of money. But you certainly do not need to own it.

I take it that you want 3' of your neighbors' land, 60 ' long(probably the lot size)
talk to him about it, he might agree to an easement that you will document with the county and you will pay what he asks for it
or if you want to buy it you will pay what he asks for it, don't make an offer, regardless of what the value might be
that 180 Sq ft might be of no use to him and he would have no problem selling it to you for little or nothing

Normally you would hire a real estate appraiser to value a property. In this case if you are able to come to an agreement on a sale price, it would not be necessary to hire a real estate appraiser.

In this transfer of the parcel of land, you would be required to have the city approve this transfer and change the lot to add the increase to your lot and decrease the lot of your neighbor.

I hope this has been of some benefit to you, good luck.

"FIGHT ON"

How are you going to buy "part" of a piece of property? Is the county going to subdivide that tax parcel just so you can buy your driveway?

He/she may not be able to sell, if the lot is too small after the sale, it's not allowed by the city.

an appraisal

You really need to consult an attorney on this one! E.g. there may be zoning ordinances, deed restrictions, or other issues in trying to re-subdivide an existing property, or in creating an easement (allowing another to use a portion of your property without actually selling that strip of land). You also need a knowledgeable & independent third party to negotiate for you.

Note that even reducing land area of a property by what seems like a "small" amount may severely impact that property's value.

Don't do anything until you have consulted an experienced real estate attorney on this. But your best bet is to redesign your notions of a driveway to keep it on your existing property. Even then, you may hit zoning, deed restrictions, etc, in going too close to your property line.

Get a real estate attorney, you will need one anyway because to do what you are planning will require the neighbor to subdivide their existing lot or create an easement.

You can hire a "Certified Real Estate Appraiser". Those are the ONLY people who are qualified to appraise a property. He would probably have to do it, calculate the cost per sq. ft. and then measure the driveway. Your neighbors might not like anyone messing with their property though so, I suggest you FIRST ask them about purchasing it and IF they might consider it, then talk about having it appraised, that you will pay for. Show them the appraisal and tell them what you think is fair and see if they agree. You are also going to have to go through a lawyer because the survey will have to be changed and approved by the building dept.