I think that the % of cash only restaurants is 80% if you take the entire population of establishments in the city. However, if you take the sub-set of restaurants that are inside the usual circles for visitors, then my guess is that your chances of using a credit card are much much higher, I would venture say 35-40%.

Having said this, I think that the OP has nothing to worry about... even if he must use cash to pay for meals at places that may not have plastic.