Google Apps Script that writes to a Spreadsheet a list of your Sites and when they were last edited (and the page that was edited).

Code.js

/**
 * For more information on using the Sites API, see
 * https://developers.google.com/apps-script/service_sites
 * 
 * TODO: "Edited by" column (is this possible?)
 *       Getting inconsistent results via Sites Services, may move to Sites API:
 *       https://developers.google.com/google-apps/sites/
 *       Can't use yet - GAS helper methods don't support OAuth 2.0
 */

var DOMAIN = "example.com"; // your Google Apps domain

// We clear and setup the sheet each time the script runs
function setUpSheet(sheet, columnNames) {
  sheet.clear();
  
  // Set Header Row
  var headersRange = sheet.getRange(1, 1, 1, columnNames.length);
  sheet.setFrozenRows(1);
  headersRange.setBackgroundColor("#DDDDDD");
  headersRange.setFontWeight("bold");
  headersRange.setHorizontalAlignment("center");
  headersRange.setValues([columnNames]);
}

function recordEdits() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheets()[0];
  
  var columnNames = ["Site", "Last Edited", "Page Edited"];
  setUpSheet(sheet, columnNames);

  var sites = SitesApp.getAllSites(DOMAIN);
  for (var site in sites) {
    var pages = sites[site].getAllDescendants();
    pages.sort(comparePageEdits).reverse(); // sort by pages' last edited date
    // First array item is now the most recently edited page
    
    // Make nice links via Sheet's HYPERLINK function
    var siteLink = "=hyperlink(\"" + sites[site].getUrl() + "\";\"" + sites[site].getTitle() + "\")";
    var latestPageLink = "=hyperlink(\"" + pages[0].getUrl() + "\";\"" + pages[0].getTitle() + "\")";
    
    sheet.appendRow([siteLink, pages[0].getLastEdited(), latestPageLink]);
  }
  
  // Sort by Last Edited column, most recent at top
  sheet.sort(2, false);
}

// Custom comparison method
function comparePageEdits(a,b) {
  if (a.getLastEdited() < b.getLastEdited())
    return -1;
  if (a.getLastEdited() > b.getLastEdited())
    return 1;
  return 0;
}