Closing can take place at a number of different locations depending on the situation. Some states, like Delaware for example, require that an attorney conduct closing and handle the title work on any real estate transaction. In this scenario closing will most likely take place at the attorneys office. There is the rare case where an attorney will do closing out of their office, however there is usually a higher fee associated with this.Most title companies will be willing to find a location that is convenient for both them and the customers, if meeting at the closing attorney's office is not an options.
The notary doesn't necessarily need to be certified, and there is no state or federal agency to oversee them being so--there are, though, entities that will 'certify' them in the handling of loan documents. Sometimes this doesn't amount to much; I've heard of notaries being 'certified' using an openbook test and being able to take it repeatedly (read open book) until they pass! Not very good certification, if you ask me!
The main thing is that they should be thoroughly experienced with the closing process. Ask them how many closings they've done overall--a good number to start at is about 500, then you know you have someone with enough experience to handle the closing right. There are really only a handful of states that are attorney-only, and while attorneys might charge more for the convenience of closing outside of a Title Company, mobile notaries do not--its is typically the same charge as if they were at the Title/Escrow office.
In most states loan closings can be conducted at any location as long as a certified notary is present to witness the signing and stamp the necessary documents.
The most common location for loan closings are title & escrow offices.
Notaries a/k/a Signing Agents/Mobile Notaries want to have contact information (cell number for after hours) for the Mortgage Broker/LO if there are questions the borrowers need answered at closing. Mobile Notaries can do the closing at a location of the borrower's choice, i.e., office, home, restaurant, library etc. and at a time the borrower chooses.
Some states are attorney states and require than an attorney be present to answer questions about the closing package and witness signatures. This is often at an additional cost to the buyer, but provides peace of mind for many to know than an uninterested third party will be present to explain and answer questions.
Many title companies will offer "in-home" closings. This is often the most convenient option for the borrower.