What journals that may consider "new proof of old results"?
The answer is certainly "yes", but to identify the best fit for your paper you'll have to decide how different your proof is from previous proofs.  It often happens that two proofs look completely different when viewed line-by-line, but still the main intermediate steps in the proofs are essentially the same -- in other words, proofs can use the same strategy but different tactics. If your main contribution is in finding an efficient or elegant way to present some of the same ideas that were used in previous proofs, then you might consider Expositiones Mathematicae or the American Mathematical Monthly.  On the other hand, if your proofs use entirely new ideas, then you have done original research and you should submit your paper to a standard journal.  In between these two extremes is L'Enseignement Mathématique, which often publishes papers which combine new research with improved exposition of known results.