There are so many variables - I've just done exactly what you mention, so these are the things I have considered:
What is my survival budget - how much do I need to "make" from the business each month to make it work?
You might need start-up capital to cover your living expenses until the profit is sufficient to live on.
What are the overheads for the business - how much does it cost to "open the door" each trading day?
Include the rent or lease, utilities, waste collection, banking charges, maintenance contracts, safety inspections, website hosting, insurance, services (wifi, merchant card etc). You might need capital to set these up/take them over and cover some of the monthly in the early months if turnover is low.
What is the age/condition of any equipment; will it need replacing soon? Allow some capital for replacing at least one of the essentials on day 1 as they are bound to go wrong at the worst possible time!
Will you be reprinting menus,redecorating, re-branding, replacing sundries such as tablecloths, displays, cutlery? This can add up - as I've recently discovered!
If the sale includes SAV (stock at valuation) then you'll need capital to cover the cost of the stock, plus extra capital available to fill the gaps - there might not be any coffee beans, tea bags in stock at the point that you buy it - I had to buy 16 different types of tea before I opened the doors, for instance!
Will you be marketing? What is currently in place to promote the business, is there a cost, and what extra advertising do you want? Press releases are great when you take over a premises, but with a lot of local rags you have to pay for a small ad alongside a half page editorial/photo!
Clothing! If you haven't got a suitable wardrobe for running a cafe every day, you'll need to buy some!
There's probably lots more, but if you want to PM me, I'll give you the warts and all story of taking over a cafe!