Ditto what everyone else has said, and here's my 2 cents:
DEFINITELY ask why they are selling? And get details! Don't just accept a pat answer...dig a little deeper with more questions phrased a little differently and see how many different answers you get. I recently tried to purchase a bakery that had closed it's doors last August. Her reason she gave me was 'health problems'...that her doctor told her she just couldn't carry on working. Ok, fair enough, I thought. She was in her 60's so that was a likely possibility.
Turned out that there were all kinds of problems...even after I gave earnest $ and signed an offer to purchase, she refused to give me a financial stmt or a copy of the books...said she 'didn't feel comfortable doing that'...???? I found out that she had opened the bakery for her daughter, really...and her daughter pretty much had the attitude of 'mamma will pay for everything' so she could just design cakes and have fun baking. I was told by a mutual friend that happened to work for Sysco that they were suing her and so was all her other suppliers. The kicker - she was trying to transfer all of her supplier accts with the sale! Though I knew I wouldn't have been held liable in the end, it sure would have been a PITA to deal with all of that after the fact. She even went as far as to lie to me about where the bakery did their banking!? I went to the same bank to talk w/them about the financing and once they realized just what business it was that I was buying...they told me they just couldn't give me the loan and they suggested that I not buy that particular business...that's all they could say since she/the bakery was a client of theirs. But the fact they said that was a HUGE warning sign to me...I backed out immediately. Turned out she owed for all of the equipment, but told me it was all paid for. So, just be really careful...find out as much as possible before you commit in any way...people are not always honest. And, as I found out, if they lie about something small...there's probably bigger problems than you could possibly imagine. Ask lots of questions, dig deep...and even ask outright - Is the business in debt in any way? If so, how much & to who? Is the business being sued by anyone? Are there any liens on any of the equipment? Who are their suppliers? Are they ok w/you contacting their suppliers to inquire about their account status? Ask for names, names, names of people/suppliers/references and call and/or meet with every one of them...if they're hiding something, you'll find out eventually. Get the name of their lawyer, acct, etc.
I would also warn against transferring the name of the bakery with the sale, unless you plan on doing the same things they did and changing very little, if anything, about the items you carry and things you do there. If the name stays the same, customers expect the same - in everything! It's harder to put your own stamp on things if you're working in the shadow of the former owner and their way of doing things. If you DO want to keep the name, make sure there isn't a separate cost for buying that name - you're also buying the 'good will' of the business, or the established clientele, when you keep a business name, so that's why sometimes the sale of the name is entirely different than the sale of the business. Also ask for all the info/warranties on all the equipment and things like that, so you're not scrambling later on if there's a problem...all the documentation to go with it too.
This woman even wanted to work for me part-time after the sale, was giving me names of 2 former employees who would want to work part-time. I know I may be bitter...but my point is, no matter how nice and honest the people seem up front, you just never know. This lady was very motherly towards me and I just never would've thought she'd be hiding sooooo much, knowing I was serious about the purchase and all the work I had to do just to PREPARE to buy that bakery.
The positive thing for you is that she's already turned over a financial stmt to you, before negotiations it seems...that's great!! But still, for your own safety (and sanity) still be extremely thorough in everything you do relating to purchasing the coffee shop...please don't assume anything and you'll be fine.