I think вiльний столик means exactly that - when you come to a restaurant and ask if there is a table available. It doesn't mean a free table for which you don't have to pay money.
Then, I think the question might be whether вілний covers all the meanings of free--available, without cost, and independent.
Вільний does mean available and independent. For "without cost" we commonly say безплатний or безкоштовний. Free entry is "вільний вхід" though
OK, of course, that could just as easily mean unobstructed entry, right?