e.g.
Indianapolis
Indianapolis, IN
Indianapolis, Indiana

Arguments:

Plain names may be preferable. The Getty TGN uses plain names, but it has some other fields which differentiate between like place names. It has a notation (a term ID number), and the broader terms up the hierarchy appear in parentheses below the term. If you need to differentiate between identical place names, you can use one of the methods described in Homographs or you can put a comma, a space, and a broader term such as the state name, to differentiate this place from others of the same name. It will be advantageous to be consistent about how you structure the term e.g. terms for towns always include the name of the state.

There's a separate issue where there are alternative names for a single place and you need to decide which one will be preferred (or at least which one will be the "Primary" term which is displayed in the Lexicon tree. Z39.19 says to prefer an official name to a popular name e.g. Netherlands vs. Holland, and to a shorter form e.g. Philippines vs. Republic of the Philippines. The general rule is to prefer the version of the name which is more likely to be familiar to your users. There's also the issue of historical place names, which the Getty TGN seems to be handling well.