What is the safest medicine for a senior citizen with mild renal failure to take for uti?

Depends. It will depend upon the organism producing the UTI and its sensitivities to antibiotics, and the nature of the UTI (upper v. Lower tract infection, simple v. Complicated, etc.) most of the antibiotics in general use today are safe, and even if they enhance renal insufficiency this is often reversible. Would, however, stay away from aminoglycosides (gentamicin, tobramycin, etc.).