Devices, systems and methods establish scaffold-like structures within the heart or a body cavity. The scaffold-like structures establish a stable platform that makes it possible to accomplish a desired therapeutic and/or diagnostic objective in a targeted fashion in one or more tissue regions. The desired therapeutic and/or diagnostic objectives can include, e.g., (i) the delivery of various chemical, drug, and/or biological agents (in liquid, gel, or wafer form) into contact on or in the tissue regions, to accomplish, e.g., ablation or other therapeutic objectives in a controlled, precise fashion; and/or (ii) the delivery of mechanical, heat, cooling, or electrical energy to the tissue region--e.g., to promote the intake by tissue of a chemical, drug, or biological agent, or to pace heart tissue, or to form temporary or permanent conduction blocks, or to otherwise achieve localized effects in targeted tissue regions such as tissue shrinkage, or combinations thereof; and/or (iii) the positioning of physiologic sensors and/or monitors to analyze heart function for diagnostic purposes, e.g., to locate the origin of ectopic pacemakers or other regions where therapeutic intervention may be indicated.