When you give the owner of the establishment your money, you are executing some of your obligations pursuant to a contract you are creating that binds you and the business owner to certain terms - whether you are paying cover to get into a club, or paying for 100 cheeseburgers at McDonald's.
Typically, you aren't going to get a written contract up-front with all of the terms and conditions that both sides are agreeing to. Contracts require a meeting of the minds to occur and, when terms of the contract are unclear, they are either held against the drafter of the contract (if one party did most of the writing of the contract) or judged based on concepts of equity, fairness, and what a reasonable person entering into such an agreement would expect.
So - what of your examples?
If you pay cover and get into a club, and "didn't do anything", presumably you would not have violated the terms of the contract that was created when you exchanged your money for access to the facilities. Their throwing you out regardless would constitute a breach and entitle you to be made whole (e.g., a refund). If they were found to act in bad faith they might even be guilty of more - either owing more to you, or fines to the government, or maybe even getting criminal charges pressed (e.g., fraud).
If you bought $100 worth of burgers at McDonald's, the situation is similar but perhaps less clearly tilted in your favor. When ordering, did you order at the counter or at a pickup window? Did you order for "here" or "to-go" when the order was placed? A judge may side with McDonald's since it may not be reasonable to eat $100 worth of food at McDonald's in a single sitting. Of course, if you can show that you made it clear you intended to stay before you exchanged money for product and that this was a part of the agreement, that might be enough to get the matter settled as a matter of contract.
When in doubt, ask yourself whether you are acting reasonably and in good faith, and if the other party is acting unreasonably or in bad faith. If both are true, you are probably entitled to be made whole - in the sense that you will be restored, at the other party's expense - either to a state prior to the agreement, or to the state you would have been in had the other party upheld its obligations.
In any case - the owners of private property can always legally require that you leave the property. What's at issue is whether they are also entitled to benefit from your having honored some of the terms (payment) of an agreement that they later chose to terminate (without just cause). You might be entitled to a refund, but you won't ever be entitled to stay against the wishes of the owner.