Get parent record fields using getRecord uiRecordApi in lwc

added based on comments

It seems there is a bug for importing geolocation fields (able to import other compound fields like BillingCity). So, we can use direct string notation as below.

Geolocation type fields are Compound Fields (like BillingAddress). Two main points to be highlighted from docs is :

Geolocation is a compound field that counts toward your org’s limits as three custom fields: one for latitude, one for longitude, and one for internal use. Support for the compound field (geolocation) versus the field’s components (latitude and longitude) varies depending on the functionality you’re using in Salesforce. For example, you can create list views that show the field and its components, but you can’t select the compound geolocation field in Apex. You can run SOQL queries only on a geolocation field’s components.

Compound fields are accessible only through the SOAP and REST APIs. The compound versions of fields aren’t accessible anywhere in the Salesforce user interface.

Below is the working sample code:

import { LightningElement, wire, api, track } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';

export default class Poc extends LightningElement {
    @api recordId;

    @wire(getRecord, {
        recordId: '$recordId',
        fields: [ 'Account.Acc_Location__Latitude__s', 'Account.Acc_Location__Longitude__s' ]
    })
    wiredAcc({ data, error }) {
        console.log('Account => ', JSON.stringify(data), JSON.stringify(error));
    }
}

and its output:

{
  "apiName": "Account",
  "childRelationships": {

  },
  "fields": {
    "Acc_Location__Latitude__s": {
      "displayValue": null,
      "value": 1.2345678
    },
    "Acc_Location__Longitude__s": {
      "displayValue": null,
      "value": 2.3456789
    }
  },
  "id": "00128000009j45sAAA",
  "lastModifiedById": "00528000001IIBvAAO",
  "lastModifiedDate": "2019-08-25T14:37:49.000Z",
  "recordTypeInfo": null,
  "systemModstamp": "2019-08-25T14:37:49.000Z"
}

Note that you should ideally use imported fields instead of direct strings in parameter

I am wondering if this is a timing issue, where you are calling testMe before the getRecord is finished, though I'd need to see your template to be sure. But I re-created your code in a scratch org, and it worked ok when I used this as my template, but without the if:true, both Name and Service Area are undefined

<template>
    <template if:true={app}>
    Test Me: {testMe}
    </template>
</template>

And my controller:

import { LightningElement, api, track, wire } from 'lwc';
import { getRecord, getFieldValue } from 'lightning/uiRecordApi';

import APP_NAME from '@salesforce/schema/Application__c.Name';
import APP_SERVICEAREA from '@salesforce/schema/Application__c.Service_Area__c';

export default class StackAppRecord extends LightningElement {
    @api recordId; // Application__c.Id
    @track app; // Application__c record
    @track appName;
    // ...
    @wire(getRecord, { recordId: '$recordId', fields: [APP_NAME,APP_SERVICEAREA] })
    loadRecord ({ error, data })   {
        if (data) {
            this.app = data;
            this.error = undefined;
            console.log('got data');
        } else if (error) {
            // ...
        }
    }
    // Called from a {testMe} in the HTML template
    get testMe() {
        console.log(this.app); // returns a Proxy
        console.log(JSON.stringify(this.app)); // returns a JSON as expected:
        console.log(this.app.fields.Name.value); // shows Name Value:
        console.log(this.app.fields.Service_Area__c.value); // show Service Value:
        return '?!';
    }

}