I would say we could probably go one step further and just offer all of this off of the parser serivces!

For example:

type ParserServices = {
  getTypeAtLocation(node: TSESTree.Node): ReturnType<ts.TypeChecker['getTypeAtLocation']>;
};

const parserServices = util.getParserServices(context);

parserServices.getTypeAtLocation(node);

That would make it even more straight-forward for people to use the tooling!

Oh interesting. I like putting this as a member of ParserServices, though I'm hesitant to put potentially dozens of them as siblings of our own properties. Maybe parserServices.checker.getTypeAtLocation?

the reason I like it as a direct sibling is it's one less step.
Right now people do things like

const {program} = util.getParserServices(context);
const checker = program.getTypeChecker();

Adding it as a separate property would make it more likely there's a clash if the consumer needs a more advanced API than what we offer.
For example:

const {checker, program} = util.getParserServices(context);
const checker2 = program.getTypeChecker();

If we build it right then most usecases shouldn't really need to ever manually touch program/esTreeNodeToTSNodeMap/tsNodeToESTreeNodeMap!