You can use the comma operator:

 {Object.keys(this.state.types).map((obj) => (
      console.log(obj), <-- This guy
      <Item label={obj[TYPE]} value={obj[ID]} />
      ))}

Which evaluates the statement and then discards it, or you can use the || operator which will evaluate console.log which returns false and then will return the React element:

 {Object.keys(this.state.types).map((obj) => console.log(obj) || (

      <Item label={obj[TYPE]} value={obj[ID]} />
      ))}

However, both are fairly hacky, I recommend you turn your arrow function into a multi-line arrow and just use return:

 {Object.keys(this.state.types).map((obj) => { 
      console.log(obj);
      return <Item label={obj[TYPE]} value={obj[ID]} />
  })}

On a side note - don't forget to set the key property on your objects returned from an array or you'll get a performance slowdown and a warning (you're currently not doing this).

The round brackets in => ( tell the function that it's returning an object (JSX is transpiled into a JS object). You want a function body to run console.log(), and then return the <Item> element.

Convert the round brackets to curly ones, and add a return statement:

{Object.keys(this.state.types).map((obj) => {
  console.log(obj); <-- This guy
  return (
    <Item label={obj[TYPE]} value={obj[ID]} />
  );
})}